Displaying similar documents to “Strong pseudocompact properties”

A note on paratopological groups

Chuan Liu (2006)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, it is proved that a first-countable paratopological group has a regular G δ -diagonal, which gives an affirmative answer to Arhangel’skii and Burke’s question [, Topology Appl. (2006), 1917–1929]. If G is a symmetrizable paratopological group, then G is a developable space. We also discuss copies of S ω and of S 2 in paratopological groups and generalize some Nyikos [, Proc. Amer. Math. Soc. (1981), no. 4, 793–801] and Svetlichnyi [, Vestnik Moskov. Univ. Ser. I Mat. Mekh....

Some properties of relatively strong pseudocompactness

Guo-Fang Zhang (2008)

Czechoslovak Mathematical Journal

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In this paper, we study some properties of relatively strong pseudocompactness and mainly show that if a Tychonoff space X and a subspace Y satisfy that Y ⊂ Int Y ¯ and Y is strongly pseudocompact and metacompact in X , then Y is compact in X . We also give an example to demonstrate that the condition Y ⊂ Int Y ¯ can not be omitted.

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...