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On a characterization of the unit interval in terms of clones

Artur Barkhudaryan (1999)

Commentationes Mathematicae Universitatis Carolinae

This paper gives a partial solution to a problem of W. Taylor on characterization of the unit interval in the class of all topological spaces by means of the first order properties of their clones. A characterization within the class of compact spaces is obtained.

On a -Kasch spaces

Ali Akbar Estaji, Melvin Henriksen (2010)

Archivum Mathematicum

If X is a Tychonoff space, C ( X ) its ring of real-valued continuous functions. In this paper, we study non-essential ideals in C ( X ) . Let a be a infinite cardinal, then X is called a -Kasch (resp. a ¯ -Kasch) space if given any ideal (resp. z -ideal) I with gen ( I ) < a then I is a non-essential ideal. We show that X is an 0 -Kasch space if and only if X is an almost P -space and X is an 1 -Kasch space if and only if X is a pseudocompact and almost P -space. Let C F ( X ) denote the socle of C ( X ) . For a topological space X with only...

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