Relatively compact subspace information

a relatively compact subspace (or relatively compact subset, or precompact subset) Y of a topological space X is a subset whose closure is compact. Every...

space Paracompact space Quasi-compact morphism Precompact set - also called totally bounded Relatively compact subspace Totally bounded Let X = {a, b}...

These are compact only if they are finite. All open or closed subsets of a locally compact Hausdorff space are locally compact in the subspace topology...

Precompact set may refer to: Relatively compact subspace, a subset whose closure is compact Totally bounded set, a subset that can be covered by finitely...

complete. Compact space Locally compact space Measure of non-compactness Orthocompact space Paracompact space Relatively compact subspace Sutherland...

wikidata descriptions as a fallback Relatively compact subspace – subset of a topological space whose closure is compactPages displaying wikidata descriptions...

bounded subsets of X {\displaystyle X} to relatively compact subsets of Y {\displaystyle Y} (subsets with compact closure in Y {\displaystyle Y} ). Such...

Baire space Banach–Mazur game Meagre set Comeagre set Compact space Relatively compact subspace Heine–Borel theorem Tychonoff's theorem Finite intersection...

In functional analysis, compact operators are linear operators on Banach spaces that map bounded sets to relatively compact sets. In the case of a Hilbert...

finite-dimensional subspace of a TVS is closed. A characterization of finite dimensionality is that a Hausdorff TVS is locally compact if and only if it...

G were compact then there is a unique decomposition of H into a countable direct sum of finite-dimensional, irreducible, invariant subspaces (this is...

with the subspace topology induced on it by f {\displaystyle f} 's codomain Y . {\displaystyle Y.} Every strongly open map is a relatively open map....

{\displaystyle K:={\overline {\operatorname {co} }}S} of this compact subset is compact. The vector subspace X := span ⁡ S = span ⁡ { e 1 , e 2 , … } {\displaystyle...

subspace of L2(D); in fact, it is a closed subspace, and so a Hilbert space in its own right. This is a consequence of the estimate, valid on compact...

{\displaystyle K} of C ( X ) {\displaystyle {\mathcal {C}}(X)} is relatively compact if and only if it is bounded in the norm of C ( X ) , {\displaystyle...

number lemma, which shows that for any open cover of a compact space, every point is relatively deep inside one of the sets of the cover. Unlike in the...

  K n − 1   {\displaystyle \ {\mathcal {K}}^{n-1}\ } is an invariant subspace of A. To see that, consider any   k ∈ K n − 1 {\displaystyle \ k\in {\mathcal...

}(U)} is endowed with the subspace topology induced on it by C i ( U ) . {\displaystyle C^{i}(U).} If the family of compact sets K = { U ¯ 1 , U ¯ 2 ...

proper if f − 1 ( C ) {\displaystyle f^{-1}(C)} is a compact set in X for any compact subspace C of Y. Proximity space A proximity space (X, d) is a...

x^{-1}\right).} However, if the unit group is endowed with the subspace topology as a subspace of R , {\displaystyle R,} it may not be a topological group...

topological space X {\displaystyle X} is called relatively compact if its closure is a compact subspace of X . {\displaystyle X.} For any topological space...

if X if infinite it is not weakly countably compact. Locally compact but not locally relatively compact. If x ∈ X {\displaystyle x\in X} , then the set...

a locally compact commutative group, then for any neighborhood N in G of the identity element, there exists a symmetric relatively compact neighborhood...

defined above for the vector subspace of a geometric algebra can be extended to cover the entire algebra. For compactness, we'll use a single capital letter...

f ( g − 1 ⋅ x ) {\displaystyle [{}_{g}f](x)=f(g^{-1}\cdot x)} is relatively compact in the uniform topology as g varies through G. Theorem. A bounded...

semi-Montel space or perfect if every bounded subset is relatively compact. A subset of a TVS is compact if and only if it is complete and totally bounded....