Remarks on aleph_1-metrizable not metrizable first countable spaces and CWH
Logic
2016-09-06 v1
Abstract
CWH, CWN stand for collectionwise Hausdorff and collectionwise normal respectively. We analyze the statement "there is a lambda-CWH not CWH first countable (Hausdorff topological) space". We prove the existence of such a space under various conditions, show its equivalence to: there is a lambda-CWN not CWN first countable space and give an equivalent set theoretic statement; the nicest version we can obtain is in \S4. The author had a flawed proof of the existence of such spaces in ZFC, for some lambda > aleph_1, in June of 1992; still we decided that there is some interest in the correct part and some additions.
Cite
@article{arxiv.math/9408202,
title = {Remarks on aleph_1-metrizable not metrizable first countable spaces and CWH},
author = {Saharon Shelah},
journal= {arXiv preprint arXiv:math/9408202},
year = {2016}
}