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See searches and references containing DENSE SET!DENSE SET
Subset whose closure is the whole space
showing that dense sets need not contain any non-empty open set. The intersection of two dense open subsets of a topological space is again dense and open
Dense_set
Mathematical set whose closure has empty interior
topological space is called nowhere dense or rare if its closure has empty interior. In a very loose sense, it is a set whose elements are not tightly clustered
Nowhere_dense_set
"Small" subset of a topological space
X} will be a topological space. The definition of meagre set uses the notion of a nowhere dense subset of X , {\displaystyle X,} that is, a subset of X
Meagre_set
Set of real numbers in mathematics
Smith–Volterra–Cantor set (SVC), ε-Cantor set, or fat Cantor set is an example of a set of points on the real line that is nowhere dense (in particular it
Smith–Volterra–Cantor_set
Does the plane contains a dense set of points whose distances are all rational
Unsolved problem in mathematics Is there a dense set of points in the plane at rational distances from each other? More unsolved problems in mathematics
Erdős–Ulam_problem
Fractal named after mathematician Benoit Mandelbrot
the Mandelbrot set. For example, Shishikura proved that, for a dense set of parameters in the boundary of the Mandelbrot set, the Julia set has Hausdorff
Mandelbrot_set
Type of ordering of a set
In mathematics, a partial order or total order < on a set X {\displaystyle X} is said to be dense if, for all x {\displaystyle x} and y {\displaystyle
Dense_order
Topological subset with no isolated point
dense-in-itself closed set is called a perfect set. (In other words, a perfect set is a closed set without isolated point.) The notion of dense set is
Dense-in-itself
Well-spaced set of points in a metric space
discrete sets, relatively dense sets, and Delone sets (named after Boris Delone) are several closely related definitions of well-spaced sets of points
Delone_set
Countable intersection of open sets
{Q} } were the intersection of open sets A n {\displaystyle A_{n}} each A n {\displaystyle A_{n}} would be dense in R {\displaystyle \mathbb {R} } because
Gδ_set
Concept in topology
(or first category) set (namely, a set that is a countable union of sets whose closure has empty interior, i.e., nowhere dense sets) and a nonmeagre (or
Baire_space
Concept in mathematical analysis
derivative of an everywhere differentiable function and that vanishes in a dense set. In particular, a Pompeiu derivative is discontinuous at every point where
Pompeiu_derivative
Fractal sets in complex dynamics of mathematics
{\displaystyle \operatorname {J} (f)} is a nowhere dense set (it is without interior points) and an uncountable set (of the same cardinality as the real numbers)
Julia_set
On topological spaces where the intersection of countably many dense open sets is dense
topological space such that the intersection of countably many dense open sets is still dense). It is used in the proof of results in many areas of analysis
Baire_category_theorem
All points in the topological closure not belonging to the interior
1]} These last two examples illustrate the fact that the boundary of a dense set with empty interior is its closure. They also show that it is possible
Boundary_(topology)
Uniqueness of countable dense linear orders
Cantor's isomorphism theorem states that every two nonempty countable dense unbounded linear orders are order-isomorphic. The theorem is named after
Cantor's_isomorphism_theorem
In mathematics, a Meyer set or almost lattice is a relatively dense set X of points in the Euclidean plane or a higher-dimensional Euclidean space such
Meyer_set
number field K {\displaystyle K} are not a dense set in Zariski topology. Erdős–Ulam problem: Is there a dense set of points in the plane all at rational
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Class of sequences of natural numbers
constructions of dense Sidon sets involve the primes". A recent result of Balasubramanian and Dutta shows that if a dense Sidon set A = { a 1 , … , a
Sidon_sequence
Order-preserving mathematical function
{\displaystyle I} . Furthermore, the set A = { x ∈ I : f ′ ( x ) > 0 } {\displaystyle A=\{x\in I:f'(x)>0\}} is dense with positive Lebesgue measure. Not
Monotonic_function
Topology on prime ideals and algebraic varieties
introduced primarily by Oscar Zariski and later generalized for making the set of prime ideals of a commutative ring (called the spectrum of the ring) a
Zariski_topology
Unsolved conjecture in geometry
{\displaystyle k} -rational points of X {\displaystyle X} do not form a dense set in the Zariski topology on X {\displaystyle X} . The general form of the
Bombieri–Lang_conjecture
Mathematical analysis of discontinuous points
it has a discontinuity there. The set of all points of discontinuity of a function may be a discrete set, a dense set, or even the entire domain of the
Classification of discontinuities
Classification_of_discontinuities
Property holding for typical examples
on a dense open set, or more generally on a residual set, with the dual concept being a closed nowhere dense set, or more generally a meagre set. There
Generic_property
Cofinal and coinitial set, sometimes also called dense Meet-dense set and join-dense set Linked set (upwards and downwards) Directed set (upwards and downwards)
List_of_order_theory_topics
countable collection of open dense sets is dense basic set theory 1. Naive set theory 2. A weak set theory, given by Kripke–Platek set theory without the axiom
Glossary_of_set_theory
Graph with almost the max amount of edges
In mathematics, a dense graph is a graph in which the number of edges is close to the maximal number of edges (where every pair of vertices is connected
Dense_graph
Set of distances defined from a set of points
Erdős–Ulam problem asks whether it is possible to have a dense set in the Euclidean plane whose distance set consists only of rational numbers. Again, it remains
Distance_set
Volume rendering technique
difference to create a dense set of 3D Gaussians that represent the scene as accurately as possible.[citation needed] An optimized set of 3D Gaussians is
Gaussian_splatting
American mathematician
of Szemerédi's theorem on the existence of polynomial progressions in dense sets of integers. She is an associate professor in the department of mathematics
Sarah_Peluse
Technique invented by Paul Cohen for proving consistency and independence results
\beta }} is dense, and a generic condition in it proves that the αth new set disagrees somewhere with the β {\displaystyle \beta } th new set. This is not
Forcing_(mathematics)
intersection of any countable collection of dense open sets is dense; see Baire space. Baire space is the set of all functions from the natural numbers
Glossary_of_general_topology
Matrix in which most of the elements are zero
contrast, if most of the elements are non-zero, the matrix is considered dense. The number of zero-valued elements divided by the total number of elements
Sparse_matrix
Nowhere dense set Null set, conull set Partition regular Piecewise syndetic set Schnirelmann density Small set (combinatorics) Stationary set Syndetic set Thick
List of exceptional set concepts
List_of_exceptional_set_concepts
Concept in mathematics
this case, structurally stable systems are typical, they form an open dense set in the space of all systems endowed with appropriate topology. In higher
Structural_stability
Method using forcing to construct sets with desired properties in computability theory
generic objects (intuitively objects that are somehow 'typical') by meeting dense sets. Both techniques are described as a relation (customarily denoted ⊩ {\displaystyle
Forcing_(computability)
Theorem in set-theoretic geometry
point is a dense set in S2.) The axiom of choice can be used to pick exactly one point from every orbit; collect these points into a set M. The action
Banach–Tarski_paradox
Fractal creation method
iterations xk stay inside the attractor and, with probability 1, form a dense set in the latter. The "chaos game" method plots points in random order all
Chaos_game
specifically in module theory, a dense submodule of a module is a refinement of the notion of an essential submodule. If N is a dense submodule of M, it may alternatively
Dense_submodule
dense set Bounded set Totally bounded set Borel set Baire set Measurable set, Non-measurable set Universally measurable set Negligible set Null set Haar
List_of_types_of_sets
Classical problem in combinatorics
s^{\prime }} is the maximum cardinality set of S {\displaystyle S} . For δ − {\displaystyle \delta -} dense instances, however, there exists a c ln
Set_cover_problem
French mathematician (1874–1932)
studied a combination of set theory and analysis topics to arrive at the Baire category theorem and the definition of a nowhere dense set. He then used these
René-Louis_Baire
Function that is discontinuous at rationals and continuous at irrationals
maximum at each rational number, providing an example of a function with a dense set of proper local maxima. See the proofs for continuity and discontinuity
Thomae's_function
{\displaystyle V} of an abelian variety A {\displaystyle A} have a Zariski dense set of torsion points. The Manin-Mumford conjecture asserts that this occurs
Bogomolov_conjecture
Mathematical conjecture
Mathematics, vol. E13, Vieweg. Oort, Frans (1997), "Canonical liftings and dense sets of CM points", in Fabrizio Catanese (ed.), Arithmetic Geometry, Cambridge:
André–Oort_conjecture
reduced form). (A dense set of discontinuities, namely the set of rational numbers.) The characteristic function of the Cantor set, which equals 1 if
Baire_function
Topics referred to by the same term
jazz saxophonist Joseph Jarman and percussionist Don Moye Dense (film), a 2004 film Dense set Concentration Flux Intensity (physics) This disambiguation
Density_(disambiguation)
Mathematical property of subsets in order theory
precisely the dense sets with respect to the right (respectively left) order topology. The cofinal relation over partially ordered sets ("posets") is
Cofinal_(mathematics)
Set of points on a line segment with certain topological properties
perfect set that is nowhere dense. More generally, in topology, a Cantor space is a topological space homeomorphic to the Cantor ternary set (equipped
Cantor_set
Branch of topology
Hausdorff space, then the interior of every union of countably many nowhere dense sets is empty. Any open subspace of a Baire space is itself a Baire space.
General_topology
On sets of points with integer distances
problem on the existence of dense point sets with rational distances. Although there can be no infinite non-collinear set of points with integer distances
Erdős–Anning_theorem
is an alternative to polygonal modeling. An object is represented by a dense set of points or viewer-facing discs holding lighting information. Surfels
Surfel
property Universally Baire set Meager set Comeager set - A comeager set is one whose complement is meager. Null set Conull set Dense set Nowhere dense set
List of properties of sets of reals
List_of_properties_of_sets_of_reals
Peptides released by neurons as intercellular messengers
are cleaved and post-translationally processed then packaged into large dense core vesicles. Neuropeptides are often co-released with other neuropeptides
Neuropeptide
First article on transfinite set theory
modified his uncountability proof by using the topological notion of a set being dense in an interval. Cantor's article also contains a proof of the existence
Cantor's first set theory article
Cantor's_first_set_theory_article
In abstract algebra, an E-dense semigroup (also called an E-inversive semigroup) is a semigroup in which every element a has at least one weak inverse
E-dense_semigroup
Linear operator on dense subset of its apparent domain
In mathematics – specifically, in operator theory – a densely defined operator or partially defined operator is a type of partially defined function.
Densely_defined_operator
Curve where spinning and moving lines cross
they cannot be solved with compass and straightedge alone. Although a dense set of points on the curve can be constructed by compass and straightedge
Quadratrix_of_Hippias
Void between celestial bodies
to the Big Bang theory, the very early universe was an extremely hot and dense state about 13.8 billion years ago which rapidly expanded. About 380,000
Outer_space
strong measure zero set is countable, is independent of ZFC. A subset X of the real line is ℵ 1 {\displaystyle \aleph _{1}} -dense if every open interval
List of statements independent of ZFC
List_of_statements_independent_of_ZFC
Highly connected subgraph
In graph theory and computer science, a dense subgraph is a subgraph with many edges per vertex. This is formalized as follows: let G = (V, E) be an undirected
Dense_subgraph
Family of RISC-based computer architectures
in-depth knowledge gained from designing the instruction set enabled the code to be very dense, making ARM BBC BASIC an extremely good test for any ARM
ARM_architecture_family
Measurable set whose measure is zero
despite being dense in R . {\displaystyle \mathbb {R} .} The standard construction of the Cantor set is an example of a null uncountable set in R ; {\displaystyle
Null_set
Type of plane curve
non-singular points form a dense set in the curve. It is also possible to construct convex curves for which the singular points are dense. A closed strictly convex
Convex_curve
Field of mathematics and science based on non-linear systems and initial conditions
transitivity implies the existence of a dense set of points in X that have dense orbits. For a chaotic system to have dense periodic orbits means that every
Chaos_theory
Mathematics award
analytic number theory, particularly with regards to polynomial patterns in dense sets." Hong Wang – "For advances on the restriction conjecture, the local smoothing
Breakthrough Prize in Mathematics
Breakthrough_Prize_in_Mathematics
Axiom in the mathematical field of set theory
satisfying the countable chain condition (hereafter ccc) and any set D = {Di}i∈I of dense subsets of P such that |D| ≤ κ, there is a filter F on P such that
Martin's_axiom
Ancient city in northwest Asia Minor
destroyed twice. After the first destruction, the citadel was rebuilt with a dense cluster of small houses on an irregular plan. The final destruction took
Troy
Unit-distance-preserving maps are isometries
distinct images. The second function maps this dense set onto a countable unit simplex, an infinite set of points all at unit distance from each other
Beckman–Quarles_theorem
2012 film by Christopher Nolan
Nolan's worst film. Anthony Lane of The New Yorker said that the "story is dense, overlong, and studded with references that will make sense only to those
The_Dark_Knight_Rises
1980 EP by Circle X
then-nascent record label Celluloid. CMJ described the album as a "raw, alien, dense set of four tuneless almost-not-even-songs made of spattered guitar, drums
Circle_X_(EP)
Role of coherent states
the existence of one such vector guarantees the existence of an entire dense set of such vectors in H {\displaystyle {\mathfrak {H}}} . Moreover, if the
Coherent states in mathematical physics
Coherent_states_in_mathematical_physics
family of maps from the complex plane to itself is hyperbolic for an open dense set of parameters. Świątek, Grzegorz; Graczyk, Jacek (1998), The real Fatou
Fatou_conjecture
category set) in only countably many points. Equivalently, A is an uncountable subset of R {\displaystyle \mathbb {R} } that meets every nowhere dense subset
Luzin_space
Vector space with a notion of nearness
union of compact convex sets is again compact and convex. Meager, nowhere dense, and Baire A disk in a TVS is not nowhere dense if and only if its closure
Topological_vector_space
German mathematician (1868–1942)
Hausdorff is also of fundamental importance: for each unbounded and ordered dense set A {\displaystyle A} there are two uniquely determined regular initial
Felix_Hausdorff
Generalised alphabetical order
of ordered symbols or, more generally, of elements of a totally ordered set. There are several variants and generalizations of the lexicographical ordering
Lexicographic_order
Indefinite integral
{\displaystyle g(x)=G'(x)=0} for all x in the set { F ( x n ) } n ≥ 1 {\displaystyle \{F(x_{n})\}_{n\geq 1}} which is dense in the interval [ F ( − 1 ) , F ( 1
Antiderivative
Mathematical set with an ordering
In mathematics, especially order theory, a partial order on a set is an arrangement such that, for certain pairs of elements, one precedes the other.
Partially_ordered_set
Special subset of a partially ordered set
collection of dense subsets (in the ordinal topology) of a, and ♣(a) meets each element of C. Replacing C with an arbitrary collection C̃ of dense sets, there
Filter_(mathematics)
Property of artificial neural networks
theorem formally states that a family of neural network functions is a dense set within a larger space of functions they are intended to approximate. In
Universal approximation theorem
Universal_approximation_theorem
American television sitcom (2007–2019)
as an official set by the Lego Ideas review board. On November 7, 2014, Lego Ideas approved the design and began refining it. The set was released in
The_Big_Bang_Theory
Basic integral in elementary calculus
equivalent to IC is Riemann integrable: g, like IC, must be zero on a dense set, so as in the previous example, any Riemann sum of g has a refinement
Riemann_integral
Enchantress-goddess in Greek mythology
described as a beautiful goddess living in a palace isolated in the midst of a dense wood on her island of Aeaea. Around her home prowl strangely docile lions
Circe
Unsolved problem in mathematics
rational field Q {\displaystyle \mathbb {Q} } . In fact this set of rational numbers is dense in Q {\displaystyle \mathbb {Q} } . The discriminant of g(y
Inverse_Galois_problem
List of World War II films List of films set in ancient Rome List of films set in ancient Greece List of films set in ancient Egypt List of films based on
List of historical films set in Near Eastern and Western civilization
List_of_historical_films_set_in_Near_Eastern_and_Western_civilization
Dynamical system involving reflection
starting positions and orientations that give rise to periodic paths form a dense set. For isosceles triangles, a path from the midpoint of the base perpendicular
Triangular_billiards
Finite sum of distinct unit fractions
fraction expansion, and showing that expansions exist for any sufficiently dense set of sufficiently smooth numbers. One of the earliest publications of Paul
Egyptian_fraction
Method of drawing geometric objects
power of two and a set of distinct Fermat primes. In addition there is a dense set of constructible angles of infinite order. Given a set of points in the
Straightedge and compass construction
Straightedge_and_compass_construction
Wealthy people who travel widely for pleasure
The jet set is a social group of wealthy and fashionable people who travel the world to participate in social activities unavailable to ordinary people
Jet_set
Numbers whose differences are not squares
MR 0466059, S2CID 122018775. Green, Ben (2002), "On arithmetic structures in dense sets of integers", Duke Mathematical Journal, 114 (2): 215–238, doi:10
Square-difference-free_set
Order whose elements are all comparable
form an initial totally ordered set which is dense in the real numbers. Moreover, the reflexive reduction < is a dense order on the rational numbers. The
Total_order
French mathematician (1923–2002)
set of topologically stable mappings between two smooth manifolds is a dense set. Thom's lectures on the stability of differentiable mappings, given at
René_Thom
Theorem of dynamical systems
F n ≠ 0 {\displaystyle dF_{1}\wedge \cdots \wedge dF_{n}\neq 0} on a dense set Mutually Poisson commuting: the Poisson bracket { F i , F j } {\displaystyle
Liouville–Arnold_theorem
Ordered chemical structure with no repeating pattern
of such a quasicrystal is nonzero only at a dense set of points spanned by integer multiples of a finite set of basis vectors, which are the projections
Quasicrystal
British mathematician (1925–2015)
it is not possible for the size of such a set to be proportional to n {\displaystyle n} : every dense set of integers contains a three-term arithmetic
Klaus_Roth
{\displaystyle z_{1},...,z_{n},e^{p(z_{1},...,z_{n})}} are all algebraic at a dense set of points of the hypersurface p = 0 {\displaystyle p=0} . Bombieri, Enrico
Schneider–Lang_theorem
Well-quasi-ordering of finite trees
mathematics, Kruskal's tree theorem states that the set of finite trees over a well-quasi-ordered set of labels is itself well-quasi-ordered under homeomorphic
Kruskal's_tree_theorem
Mathematical lemma
subset E of a poset (P, ≤) is called dense in P if for any p ∈ P there is e ∈ E with e ≤ p. If D is a set of dense subsets of P, then a filter F in P is
Rasiowa–Sikorski_lemma
2006 film by Christopher Nolan
made the outwardly straightforward comic book adaptation (Batman Begins) dense and sophisticated ... any truly great performance is almost as much showmanship
The_Prestige
DENSE SET
DENSE SET
Girl/Female
Indian
Girl/Female
American, Australian, British, English, Greek
Combination of Deana and Dina
Boy/Male
Christian, Indian
From Dionysisu; God of Wine
Boy/Male
Greek
God of wine.
Girl/Female
Greek
Form of Danae; the mythological mother of Perseus by Zeus.
Girl/Female
Christian & English(British/American/Australian)
Form of Dennis
Girl/Female
English American French
From the Latin Dionysos or Dionysus, referring to the Greek god of wine.
Girl/Female
Australian, Greek
The Mythological Mother of Perseus by Zeus; Form of Danae
Girl/Female
French
Feminine of Denis from the Greek name Dionysus.
Surname or Lastname
English (Kent)
English (Kent) : variant spelling of Denn.
Girl/Female
American, Australian, French, Greek
Mountain of Zeus; Feminine of Dennis; Follower of Dionysius
Girl/Female
American, Australian, British, Chinese, Christian, Danish, Dutch, English, French, German, Greek, Indian, Portuguese, Swedish, Swiss
God of Wine; Feminine of Dennis; To Advise; Alone; Nun; Solitary; Follower of Dionysus
Boy/Male
Australian, German, Greek, Hungarian
God of Wine; Wine; Drama; Follower of Dionysus
Girl/Female
Hindu, Indian
People who Give
Male
English
Variant spelling of English Dean, DENE means "dean, ecclesiastical supervisor."
Surname or Lastname
English
English : ethnic name for someone from Denmark, from Middle English den(s)ch ‘Danish’ (Old English denisc). There were many Danes in England in the Middle Ages, not only the long-established settlers in the Danelaw region, but also more recent immigrants.
Boy/Male
American, Anglo, Australian, British, Christian, English
From the Valley; Place Name; Valley; Occupational Name; Church Official
Female
English
Feminine form French Denis, DENISE means "follower of Dionysos."
Girl/Female
English
Combination of Deana (divine) and Dina (from the valley; avenged).
Boy/Male
English
From the valley.
DENSE SET
DENSE SET
Girl/Female
Muslim/Islamic
Preserved Strong
Boy/Male
Arabic, Muslim
Servant of the Descender
Boy/Male
English
From the stone fortress.
Girl/Female
Indian, Kannada
Love
Girl/Female
Australian, Celtic, Christian, Welsh
Of the White Brow; White and Smooth; Soft; Fair; Holy
Biblical
same as Mattaniah
Boy/Male
Indian
A mighty ruler
Boy/Male
American, Anglo, British, English
From the Crane Meadow; Meadow with the Cranes
Boy/Male
Hindu
Girl/Female
Australian, Spanish
Grace; Favor; Similar to Anna
DENSE SET
DENSE SET
DENSE SET
DENSE SET
DENSE SET
n.
Condition; rank.
n.
A census; -- also, a public rate or tax.
v. t.
Perception through the intellect; apprehension; recognition; understanding; discernment; appreciation.
v. t.
That which is felt or is held as a sentiment, view, or opinion; judgment; notion; opinion.
a.
Stupid; gross; crass; as, dense ignorance.
v. t.
A faculty, possessed by animals, of perceiving external objects by means of impressions made upon certain organs (sensory or sense organs) of the body, or of perceiving changes in the condition of the body; as, the senses of sight, smell, hearing, taste, and touch. See Muscular sense, under Muscular, and Temperature sense, under Temperature.
v. t.
One of two opposite directions in which a line, surface, or volume, may be supposed to be described by the motion of a point, line, or surface.
a.
Stretched tightly; strained to stiffness; rigid; not lax; as, a tense fiber.
n.
One of the forms which a verb takes by inflection or by adding auxiliary words, so as to indicate the time of the action or event signified; the modification which verbs undergo for the indication of time.
a.
Having the constituent parts massed or crowded together; close; compact; thick; containing much matter in a small space; heavy; opaque; as, a dense crowd; a dense forest; a dense fog.
v. t.
To grace.
v. t.
Sound perception and reasoning; correct judgment; good mental capacity; understanding; also, that which is sound, true, or reasonable; rational meaning.
n.
Manliness; dignity; comeliness; civility.
v. t.
To perceive by the senses; to recognize.
v. t.
Perception by the sensory organs of the body; sensation; sensibility; feeling.
v. t.
Meaning; import; signification; as, the true sense of words or phrases; the sense of a remark.
v. t.
Moral perception or appreciation.
v. i.
To burn or scatter incense.
v. t.
To perfume with odors from burning gums and spices.