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Displaying similar documents to “Categories of topological spaces with sufficiently many sequentially closed spaces”

Some results on sequentially compact extensions

Maria Cristina Vipera (1998)

Commentationes Mathematicae Universitatis Carolinae

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The class of Hausdorff spaces (or of Tychonoff spaces) which admit a Hausdorff (respectively Tychonoff) sequentially compact extension has not been characterized. We give some new conditions, in particular, we prove that every Tychonoff locally sequentially compact space has a Tychonoff one-point sequentially compact extension. We also give some results about extension of functions and about lattice properties of the family of all minimal sequentially compact extensions of a given space. ...

Hausdorff Fréchet closure spaces with maximum topological defect

Riccardo Ghiloni (2002)

Bollettino dell'Unione Matematica Italiana

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It is well-known that the topological defect of every Fréchet closure space is less than or equal to the first uncountable ordinal number ω 1 . In the case of Hausdorff Fréchet closure spaces we obtain some general conditions sufficient so that the topological defect is exactly ω 1 . Some classical and recent results are deduced from our criterion.