On -in-countable bases
S. A. Peregudov (2000)
Commentationes Mathematicae Universitatis Carolinae
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Some results concerning spaces with countably weakly uniform bases are generalized for spaces with -in-countable ones.
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S. A. Peregudov (2000)
Commentationes Mathematicae Universitatis Carolinae
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Some results concerning spaces with countably weakly uniform bases are generalized for spaces with -in-countable ones.
Cascales, B., Orihuela, J. (1991)
Portugaliae mathematica
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Hanbiao Yang (2012)
Commentationes Mathematicae Universitatis Carolinae
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For a Tychonoff space , let be the family of hypographs of all continuous maps from to endowed with the Fell topology. It is proved that has a dense separable metrizable locally compact open subset if is metrizable. Moreover, for a first-countable space , is metrizable if and only if itself is a locally compact separable metrizable space. There exists a Tychonoff space such that is metrizable but is not first-countable.
Liang-Xue Peng, Yu-Feng He (2012)
Czechoslovak Mathematical Journal
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In this note we first give a summary that on property of a remainder of a non-locally compact topological group in a compactification makes the remainder and the topological group all separable and metrizable. If a non-locally compact topological group has a compactification such that the remainder of belongs to , then and are separable and metrizable, where is a class of spaces which satisfies the following conditions: (1) if , then every compact subset of the...