Resolvability and complete accumulation points
General Topology
2023-01-31 v1
Abstract
We prove that: I. For every regular Lindel\"of space if and , then is maximally resolvable; II. For every regular countably compact space if and , then is maximally resolvable. Here , the dispersion character of , is the minimum cardinality of a nonempty open subset of . Statements I and II are corollaries of the main result: for every regular space if and every set of cardinality has a complete accumulation point, then is maximally resolvable. Moreover, regularity here can be weakened to -regularity, and the Lindel\"of property can be weakened to the linear Lindel\"of property.
Keywords
Cite
@article{arxiv.2301.12748,
title = {Resolvability and complete accumulation points},
author = {A. E. Lipin},
journal= {arXiv preprint arXiv:2301.12748},
year = {2023}
}