Displaying similar documents to “Some properties of relatively strong pseudocompactness”

A note on k-c-semistratifiable spaces and strong β -spaces

Li-Xia Wang, Liang-Xue Peng (2011)

Mathematica Bohemica

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Recall that a space X is a c-semistratifiable (CSS) space, if the compact sets of X are G δ -sets in a uniform way. In this note, we introduce another class of spaces, denoting it by k-c-semistratifiable (k-CSS), which generalizes the concept of c-semistratifiable. We discuss some properties of k-c-semistratifiable spaces. We prove that a T 2 -space X is a k-c-semistratifiable space if and only if X has a g function which satisfies the following conditions: (1) For each x ∈ X , { x } = ⋂ { g ( x , n ) : n ∈ ℕ } and g ( x , n + 1 ) ⊆ g ( x , n ) for each...

Indiscernibles and dimensional compactness

C. Ward Henson, Pavol Zlatoš (1996)

Commentationes Mathematicae Universitatis Carolinae

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This is a contribution to the theory of topological vector spaces within the framework of the alternative set theory. Using indiscernibles we will show that every infinite set u S ⊆ G in a biequivalence vector space 〈 W , M , G 〉 , such that x - y ∉ M for distinct x , y ∈ u , contains an infinite independent subset. Consequently, a class X ⊆ G is dimensionally compact iff the π -equivalence ≐ M is compact on X . This solves a problem from the paper [NPZ 1992] by J. Náter, P. Pulmann and the second author.

On k -spaces and k R -spaces

Jinjin Li (2005)

Czechoslovak Mathematical Journal

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In this note we study the relation between k R -spaces and k -spaces and prove that a k R -space with a σ -hereditarily closure-preserving k -network consisting of compact subsets is a k -space, and that a k R -space with a point-countable k -network consisting of compact subsets need not be a k -space.