Displaying similar documents to “Minimal sequential Hausdorff spaces.”

On minimal strongly KC-spaces

Weihua Sun, Yuming Xu, Ning Li (2009)

Czechoslovak Mathematical Journal

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In this article we introduce the notion of strongly KC -spaces, that is, those spaces in which countably compact subsets are closed. We find they have good properties. We prove that a space ( X , τ ) is maximal countably compact if and only if it is minimal strongly KC , and apply this result to study some properties of minimal strongly KC -spaces, some of which are not possessed by minimal KC -spaces. We also give a positive answer to a question proposed by O. T. Alas and R. G. Wilson, who asked whether...

More on strongly sequential spaces

Frédéric Mynard (2002)

Commentationes Mathematicae Universitatis Carolinae

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Strongly sequential spaces were introduced and studied to solve a problem of Tanaka concerning the product of sequential topologies. In this paper, further properties of strongly sequential spaces are investigated.

On minimal Hausdorff and minimal Urysohn functions

Filippo Cammaroto, Andrei Catalioto, Jack Porter (2011)

Open Mathematics

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In this article, we extend the work on minimal Hausdorff functions initiated by Cammaroto, Fedorchuk and Porter in a 1998 paper. Also, minimal Urysohn functions are introduced and developed. The properties of heredity and productivity are examined and developed for both minimal Hausdorff and minimal Urysohn functions.

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. ...