-proximity spaces
Giuseppe Di Maio, Somashekhar Naimpally (1991)
Czechoslovak Mathematical Journal
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Giuseppe Di Maio, Somashekhar Naimpally (1991)
Czechoslovak Mathematical Journal
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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.
Aleksander V. Arhangel'skii (2010)
Commentationes Mathematicae Universitatis Carolinae
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Some strong versions of the Fréchet-Urysohn property are introduced and studied. We also strengthen the concept of countable tightness and generalize the notions of first-countability and countable base. A construction of a topological space is described which results, in particular, in a Tychonoff countable Fréchet-Urysohn space which is not first-countable at any point. It is shown that this space can be represented as the image of a countable metrizable space under a continuous pseudoopen...
Raushan Z. Buzyakova (2006)
Commentationes Mathematicae Universitatis Carolinae
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We introduce a notion of absolute submetrizability (= ``every Tychonoff subtopology is submetrizable'') and investigate its behavior under basic topological operations. The main result is an example of an absolutely submetrizable space that contains an uncountable set of isolated points (hence the space is neither separable nor hereditarily Lindelöf). This example is used to show that absolute submetrizability is not preserved by some topological operations, in particular, by free sums. ...