Two results on special points

Volume 176 / 2003

Alan Dow Fundamenta Mathematicae 176 (2003), 171-179 MSC: Primary 54G05. DOI: 10.4064/fm176-2-5


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.


  • Alan DowDepartment of Mathematics
    University of North Carolina at Charlotte
    9201 University City Boulevard
    Charlotte, NC 28262-001, U.S.A.

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