We show that there is a nowhere ccc σ-compact space which has a remote point. We show that it is consistent to have a non-compact σ-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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm176-2-5,
author = {Alan Dow},
title = {Two results on special points},
journal = {Fundamenta Mathematicae},
volume = {177},
year = {2003},
pages = {171-179},
zbl = {1041.54033},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm176-2-5}
}
Alan Dow. Two results on special points. Fundamenta Mathematicae, Tome 177 (2003) pp. 171-179. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm176-2-5/