Displaying similar documents to “Spaces for which the diagonal has a closed neighborhood base”

A generalization of Magill's Theorem for non-locally compact spaces

Gary D. Faulkner, Maria Cristina Vipera (1995)

Commentationes Mathematicae Universitatis Carolinae

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In the theory of compactifications, Magill's theorem that the continuous image of a remainder of a space is again a remainder is one of the most important theorems in the field. It is somewhat unfortunate that the theorem holds only in locally compact spaces. In fact, if all continuous images of a remainder are again remainders, then the space must be locally compact. This paper is a modification of Magill's result to more general spaces. This of course requires restrictions on the nature...

A basic approach to the perfect extensions of spaces

Giorgio Nordo (1997)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we generalize the notion of of a Tychonoff space to a generic extension of any space by introducing the concept of . This allow us to simplify the treatment in a basic way and in a more general setting. Some [S 1 ], [S 2 ], and [D]’s results are improved and new characterizations for perfect (Hausdorff) extensions of spaces are obtained.