Increasing chains and discrete reflection of cardinality
General Topology
2015-05-26 v1
Abstract
Combining ideas from two of our previous papers, we refine Arhangel'skii Theorem by proving a cardinal inequality of which this is a special case: any increasing union of strongly discretely Lindelof spaces with countable free sequences and countable pseudocharacter has cardinality at most continuum. We then give a partial positive answer to a problem of Alan Dow on reflection of cardinality by closures of discrete sets.
Keywords
Cite
@article{arxiv.1505.06251,
title = {Increasing chains and discrete reflection of cardinality},
author = {Santi Spadaro},
journal= {arXiv preprint arXiv:1505.06251},
year = {2015}
}