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Weakly compact information


Weakly compact can refer to:

  • Weakly compact cardinal, an infinite cardinal number on which every binary relation has an equally large homogeneous subset
  • 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, for example:
    • Sequentially compact space, a set in which every infinite sequence has a convergent subsequence
    • Limit point compact, a set in which every infinite subset of X has a limit point

and 21 Related for: Weakly compact information

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Weakly compact

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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...

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Weakly compact cardinal

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

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Weak topology

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

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Locally compact space

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

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Banach space

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{\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...

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Woodin cardinal

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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...

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Polar topology

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

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List of large cardinal properties

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

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Tightness of measures

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

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Strongly compact cardinal

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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...

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Limit point compact

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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...

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Grothendieck space

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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...

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Ineffable cardinal

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

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Positive set theory

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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...

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Reflexive space

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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...

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Compact space

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

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Aronszajn tree

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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...

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Dual topology

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

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Compact cardinal

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Compact cardinal may refer to: Weakly compact cardinal Subcompact cardinal Supercompact cardinal Strongly compact cardinal This article includes a list...

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Glossary of set theory

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Vopěnka's principle holds for Vκ weakly 1.  A weakly inaccessible cardinal is a regular weak limit cardinal 2.  A weakly compact cardinal is a cardinal κ (usually...

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Weakly harmonic function

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is weakly harmonic if and only if it is harmonic. Thus weakly harmonic is actually equivalent to the seemingly stronger harmonic condition. Weak solution...

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