Weakly compact information

Weakly compact set, a compact set in a space with the weak topology Weakly compact set, a set that has some but not all of the properties of compact sets...

In mathematics, a weakly compact cardinal is a certain kind of cardinal number introduced by Erdős & Tarski (1961); weakly compact cardinals are large...

vector space weakly closed (respectively, weakly compact, etc.) if they are closed (respectively, compact, etc.) with respect to the weak topology. Likewise...

that compact subsets of Hausdorff spaces are closed, and closed subsets of compact spaces are compact. Spaces satisfying (1) are also called weakly locally...

{\displaystyle X} has a weakly convergent subsequence. A weakly compact subset A {\displaystyle A} in ℓ 1 {\displaystyle \ell ^{1}} is norm-compact. Indeed, every...

{\displaystyle M} is sequentially weakly compact. We say the family M {\displaystyle M} of probability measures is sequentially weakly compact if for every sequence...

{\displaystyle Y} carry their weak topologies. If G ′ {\displaystyle {\mathcal {G}}'} was the set of all convex balanced weakly compact equicontinuous subsets...

Aleph number) worldly cardinals weakly and strongly inaccessible, α-inaccessible, and hyper inaccessible cardinals weakly and strongly Mahlo, α-Mahlo, and...

is a Mahlo cardinal. However, the first Woodin cardinal is not even weakly compact. The hierarchy V α {\displaystyle V_{\alpha }} (known as the von Neumann...

to λ-compactness. A cardinal is weakly compact if and only if it is κ-compact; this was the original definition of that concept. Strong compactness implies...

<\gamma } . An ordinal α {\displaystyle \alpha } is called recursively weakly compact if it is Π 3 {\displaystyle \Pi _{3}} -reflecting, or equivalently,...

mathematics, a weak Hausdorff space or weakly Hausdorff space is a topological space where the image of every continuous map from a compact Hausdorff space...

also equivalent to compactness for first-countable uniform spaces). (X, d) is limit point compact (also called weakly countably compact); that is, every...

weakly compact, that is, the image of a bounded subset of X {\displaystyle X} is a weakly compact subset of Y . {\displaystyle Y.} for every weakly compactly...

κ is weakly compact then no κ-Aronszajn trees exist. Conversely, if κ is inaccessible and no κ-Aronszajn trees exist, then κ is weakly compact. An Aronszajn...

strength of Morse–Kelley set theory with the proper class ordinal a weakly compact cardinal. The universal set is a proper set in this theory. The sets...

of H, the closed unit ball B is weakly compact. Also, the compactness of T means (see above) that T : X with the weak topology → X with the norm topology...

topological space X {\displaystyle X} is said to be limit point compact or weakly countably compact if every infinite subset of X {\displaystyle X} has a limit...

are weakly closed, it follows from the third property that closed bounded convex subsets of a reflexive space X {\displaystyle X} are weakly compact. Thus...

topology, the topology of uniform convergence on all absolutely convex weakly compact subsets of X ′ {\displaystyle X'} . Given a dual pair ( X , X ′ ) {\displaystyle...

compact sets. X {\displaystyle X} is σ-compact and weakly locally compact. X {\displaystyle X} is Lindelöf and weakly locally compact. (where weakly locally...

\setminus X\in {\mathcal {F}}} . This is similar to a characterization of weakly compact cardinals. More generally, κ {\displaystyle \kappa } is called n {\displaystyle...