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Displaying similar documents to “ k -systems, k -networks and k -covers”

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.

Closed mapping theorems on k -spaces with point-countable k -networks

Alexander Shibakov (1995)

Commentationes Mathematicae Universitatis Carolinae

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We prove some closed mapping theorems on k -spaces with point-countable k -networks. One of them generalizes Lašnev’s theorem. We also construct an example of a Hausdorff space U r with a countable base that admits a closed map onto metric space which is not compact-covering. Another our result says that a k -space X with a point-countable k -network admitting a closed surjection which is not compact-covering contains a closed copy of U r .

A note on transitively D -spaces

Liang-Xue Peng (2011)

Czechoslovak Mathematical Journal

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In this note, we show that if for any transitive neighborhood assignment φ for X there is a point-countable refinement ℱ such that for any non-closed subset A of X there is some V ∈ ℱ such that | V ∩ A | ≥ ω , then X is transitively D . As a corollary, if X is a sequential space and has a point-countable w c s * -network then X is transitively D , and hence if X is a Hausdorff k -space and has a point-countable k -network, then X is transitively D . We prove that if X is a countably compact sequential space and...