Displaying similar documents to “ s n -metrizable spaces and related matters.”

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 .

Spaces with σ -locally countable weak-bases

Zhaowen Li (2006)

Archivum Mathematicum

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In this paper, spaces with σ -locally countable weak-bases are characterized as the weakly open msss-images of metric spaces (or g -first countable spaces with σ -locally countable c s -networks).