Precompact set information

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...

of the ambient space). The term precompact (or pre-compact) is sometimes used with the same meaning, but precompact is also used to mean relatively compact...

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

compact sets Lindelöf space Metacompact space Noetherian topological space Orthocompact space Paracompact space Quasi-compact morphism Precompact set - also...

In a Hausdorff locally convex TVS, the convex hull of a precompact set is again precompact. Consequently, in a complete Hausdorff locally convex space...

approximation property, if the identity map can be approximated, uniformly on precompact sets, by continuous linear maps of finite rank. For a locally convex space...

X'} has compact closure in the topology of uniform convergence on precompact sets. Furthermore, this topology on K {\displaystyle K} coincides with the...

In a Hausdorff locally convex TVS, the convex hull of a precompact set is again precompact. Consequently, in a complete locally convex Hausdorff TVS...

asymptotically Schwarzschild in the following sense: Suppose that K is an open precompact subset of M such that there is a diffeomorphism Φ : ℝ3 − B1(0) → M − K...

pointwise convergence; (3) the topology of precompact convergence. By letting G {\displaystyle {\mathcal {G}}} be the set of all compact subsets of X , {\displaystyle...

metric uses the existence of a pre-compact open set around any point. In the infinite case, open sets are no longer pre-compact and so this statement...

probability measures on X {\displaystyle X} is tight if and only if it is precompact in the topology of weak convergence. Consider the real line R {\displaystyle...

})<\epsilon } . A metric space P {\displaystyle P} is conditionally compact (or precompact), if for any ϵ > 0 {\displaystyle \epsilon >0} there exists a finite ϵ...

continuous function on X is (weakly) almost periodic if its orbit is (weakly) precompact in the Banach space C ( X ) {\displaystyle C(X)} . In speech processing...

and totally bounded (for Hausdorff TVSs, a set being totally bounded is equivalent to it being precompact). But if the TVS is not Hausdorff then there...

nuclear. Every bounded subset of a nuclear space is precompact (recall that a set is precompact if its closure in the completion of the space is compact)...

The least such r is called the diameter of M. The space M is called precompact or totally bounded if for every r > 0 there is a finite cover of M by...

} The weak maximum principle, in this setting, says that for any open precompact subset M of the domain of u, the maximum of u on the closure of M is achieved...

c ( Ω ) {\displaystyle {\mathcal {O}}_{c}(\Omega )} as the set of all precompact open subsets of Ω {\displaystyle \Omega } with respect to the standard...

{F}}({\mathcal {U}})} converges to u {\displaystyle u} uniformly on every precompact subset of X . {\displaystyle X.} Cone-saturated Positive linear functional –...