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searching for Subspace topology 41 found (149 total)

Ptak space (739 words) [view diff] exact match in snippet view article find links to article

closed in A {\displaystyle A} (when A {\displaystyle A} is given the subspace topology from X σ ′ {\displaystyle X_{\sigma }^{\prime }} ) for each equicontinuous

Discrete group (899 words) [view diff] exact match in snippet view article find links to article

group G is a discrete subgroup if H is discrete when endowed with the subspace topology from G. In other words there is a neighbourhood of the identity in

LF-space (2,771 words) [view diff] exact match in snippet view article find links to article

then the LF-space is called a strict LF-space. This means that the subspace topology induced on Xn by Xn+1 is identical to the original topology on Xn

Knaster–Kuratowski fan (302 words) [view diff] exact match in snippet view article find links to article

∈ C X c {\displaystyle \bigcup _{c\in C}X_{c}} equipped with the subspace topology inherited from the standard topology on R 2 {\displaystyle \mathbb

Invariance of domain (1,095 words) [view diff] exact match in snippet view article find links to article

\mathbb {R} ^{n},} and not just in the subspace topology. Openness of V {\displaystyle V} in the subspace topology is automatic.) Both of these statements

Weil group (983 words) [view diff] exact match in snippet view article find links to article

not have the subspace topology, but rather a finer topology. This topology is defined by giving the inertia subgroup its subspace topology and imposing

Open set (4,574 words) [view diff] exact match in snippet view article find links to article

be given its own topology (called the 'subspace topology') defined by "a set U is open in the subspace topology on Y if and only if U is the intersection

Cardinal function (2,105 words) [view diff] exact match in snippet view article find links to article

| : Y ⊆ X with the subspace topology is discrete } {\displaystyle s(X)=\sup\{|Y|:Y\subseteq X{\text{ with the subspace topology is discrete}}\}} where

Fuchsian model (662 words) [view diff] exact match in snippet view article find links to article

\mapsto (\rho (g_{1}),\ldots ,\rho (g_{r}))} . Then we give it the subspace topology. The Nielsen isomorphism theorem (this is not standard terminology

Clopen set (785 words) [view diff] exact match in snippet view article find links to article

\mathbb {R} .} The topology on X {\displaystyle X} is inherited as the subspace topology from the ordinary topology on the real line R . {\displaystyle \mathbb

Completely metrizable space (749 words) [view diff] exact match in snippet view article find links to article

it is homeomorphic to R. The space Q of rational numbers with the subspace topology inherited from R is metrizable but not completely metrizable. A topological

Metrizable space (865 words) [view diff] exact match in snippet view article find links to article

countably infinite product of the unit interval (with its natural subspace topology from the reals) with itself, endowed with the product topology. A

Limit point compact (983 words) [view diff] exact match in snippet view article find links to article

limit point are exactly those that are closed and discrete in the subspace topology. So a space is limit point compact if and only if all its closed discrete

T1 space (1,922 words) [view diff] exact match in snippet view article find links to article

the sense that each point has a T1 neighbourhood (when given the subspace topology), is also T1. Similarly, a space that is locally R0 is also R0. In

Weak Hausdorff space (718 words) [view diff] exact match in snippet view article find links to article

Hausdorff subspaces preserves the compact Hausdorff subspaces and their subspace topology requires that the space be k-Hausdorff; weak Hausdorff is not enough

Extreme point (2,071 words) [view diff] exact match in snippet view article find links to article

extreme points of a compact convex set form a Baire space (with the subspace topology) but this set may fail to be closed in X . {\displaystyle X.} The

Injective tensor product (8,577 words) [view diff] exact match in snippet view article find links to article

Im ⁡ L = L ( X ) {\displaystyle \operatorname {Im} L=L(X)} has the subspace topology induced by Y {\displaystyle Y} If S {\displaystyle S} is a subspace

Weak topology (3,110 words) [view diff] no match in snippet view article find links to article

subset of its continuous dual space, then H endowed with the weak* (subspace) topology is a metrizable topological space. However, for infinite-dimensional

Algebraic geometry and analytic geometry (2,517 words) [view diff] exact match in snippet view article find links to article

is called the "complex topology" (and is very different from the subspace topology). Suppose φ: X → Y is a morphism of schemes of locally finite type

Alexandrov topology (2,160 words) [view diff] exact match in snippet view article find links to article

point x {\displaystyle x} , in U {\displaystyle U} itself with the subspace topology any open cover of U {\displaystyle U} contains a neighbourhood of

Topologies on spaces of linear maps (6,521 words) [view diff] exact match in snippet view article find links to article

pointwise convergence on F {\displaystyle F} is identical to the subspace topology that F {\displaystyle F} inherits from Y T {\displaystyle Y^{T}} when

Alexandroff extension (2,227 words) [view diff] exact match in snippet view article find links to article

compact topology such that X {\displaystyle X} is dense in it and the subspace topology on X {\displaystyle X} induced from X ∗ {\displaystyle X^{*}} is the

Configuration space (mathematics) (2,267 words) [view diff] exact match in snippet view article

{\text{for some }}i\neq j\}.} This space is generally endowed with the subspace topology from the inclusion of Conf n ⁡ ( X ) {\displaystyle \operatorname

Homotopy fiber (1,848 words) [view diff] exact match in snippet view article find links to article

(0)=f(a)} . We give E f {\displaystyle E_{f}} a topology by giving it the subspace topology as a subset of A × B I {\displaystyle A\times B^{I}} (where B I {\displaystyle

Relative homology (2,455 words) [view diff] exact match in snippet view article find links to article

I)/(X\times \{0\}),} where X × { 0 } {\displaystyle X\times \{0\}} has the subspace topology. Then, the origin x 0 = 0 {\displaystyle x_{0}=0} is the equivalence

Projective tensor product (2,503 words) [view diff] exact match in snippet view article find links to article

{\displaystyle Z\otimes _{\pi }Y} has in general a coarser topology than the subspace topology inherited from X ⊗ π Y {\displaystyle X\otimes _{\pi }Y} ). If E {\displaystyle

Irrational number (5,252 words) [view diff] exact match in snippet view article find links to article

disconnected metrizable space. In fact, the irrationals equipped with the subspace topology have a basis of clopen groups so the space is zero-dimensional. Brjuno

Nuclear operator (4,775 words) [view diff] exact match in snippet view article find links to article

L {\displaystyle \operatorname {Im} L} , the image of L, has the subspace topology induced by Y. If S is a subspace of X then both the quotient map X

Affine variety (4,125 words) [view diff] exact match in snippet view article find links to article

an affine subvariety of kn the Zariski topology on V is simply the subspace topology inherited from the Zariski topology on kn. The geometric structure

Tautological bundle (2,441 words) [view diff] exact match in snippet view article find links to article

point V of the Grassmannian and a vector v in V; it is given the subspace topology of the Cartesian product G n ( R n + k ) × R n + k . {\displaystyle

Inductive tensor product (2,095 words) [view diff] exact match in snippet view article find links to article

\operatorname {Im} L,} the image of L , {\displaystyle L,} has the subspace topology induced by Y . {\displaystyle Y.} If S ⊆ X {\displaystyle S\subseteq

Surjection of Fréchet spaces (1,855 words) [view diff] exact match in snippet view article find links to article

induced by X {\displaystyle X} and E {\displaystyle E} is given the subspace topology induced by X ′ {\displaystyle X^{\prime }} ). Theorem — On the dual

Equicontinuity (3,745 words) [view diff] exact match in snippet view article find links to article

{\displaystyle X_{\sigma }^{\prime }} is a compact metrizable space (under the subspace topology). If in addition X {\displaystyle X} is metrizable then X σ ′ {\displaystyle

Complex geometry (3,677 words) [view diff] exact match in snippet view article find links to article

{\displaystyle X} to have a topology that is locally equivalent to the subspace topology due to the identification with open subsets of C n {\displaystyle

Polar set (4,897 words) [view diff] exact match in snippet view article find links to article

convergence so when X # {\displaystyle X^{\#}} is endowed with the subspace topology, then X # {\displaystyle X^{\#}} becomes a Hausdorff complete locally

Polyadic space (3,615 words) [view diff] exact match in snippet view article find links to article

_{T}:T{\text{ is a centred subcollection of }}{\mathcal {S}}\}} , with the subspace topology from 2 S {\displaystyle 2^{\mathcal {S}}} . We say that a space X

Differentiable vector–valued functions from Euclidean space (3,994 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \Omega } rather than K {\displaystyle K} ) and give it the subspace topology induced by C k ( Ω ; Y ) . {\displaystyle C^{k}(\Omega ;Y).} If K

Sheaf (mathematics) (10,838 words) [view diff] exact match in snippet view article

{\displaystyle E} . Notice that each stalk has the discrete topology as subspace topology. Two morphisms between sheaves determine a continuous map of the corresponding

Continued fraction (9,866 words) [view diff] exact match in snippet view article find links to article

the Baire space to the space of irrational real numbers (with the subspace topology inherited from the usual topology on the reals). The infinite continued

Complete topological vector space (15,843 words) [view diff] exact match in snippet view article find links to article

{\displaystyle X,} where I {\displaystyle I} is endowed with its subspace topology induced by X {\displaystyle X} (so that I {\displaystyle I} has the

Representation theory of the Lorentz group (19,750 words) [view diff] exact match in snippet view article find links to article

Lie subgroup of the compact group U(V). This is impossible with the subspace topology on u(G) ⊂ U(V) since all embedded Lie subgroups of a Lie group are