Two results on special points

Alan Dow¹

¹ Department of Mathematics University of North Carolina at Charlotte 9201 University City Boulevard Charlotte, NC 28262-001, U.S.A.

Fundamenta Mathematicae, Tome 176 (2003) no. 2, pp. 171-179.

Résumé

We show that there is a nowhere ccc $\sigma $-compact space which has a remote point. We show that it is consistent to have a non-compact $\sigma $-compact separable space $X$ such that every point of the remainder is a limit of a countable discrete subset of non-isolated points of $X$. This example shows that one cannot prove in ZFC that every locally compact non-compact space has discrete weak $P$-points.

Détail

DOI : 10.4064/fm176-2-5

Keywords: there nowhere ccc sigma compact space which has remote point consistent have non compact sigma compact separable space every point remainder limit countable discrete subset non isolated points example shows cannot prove zfc every locally compact non compact space has discrete weak p points