English

Resolvability and complete accumulation points

General Topology 2023-01-31 v1

Abstract

We prove that: I. For every regular Lindel\"of space XX if X=Δ(X)|X|=\Delta(X) and cfXω\mathrm{cf}|X|\ne\omega, then XX is maximally resolvable; II. For every regular countably compact space XX if X=Δ(X)|X|=\Delta(X) and cfX=ω\mathrm{cf}|X|=\omega, then XX is maximally resolvable. Here Δ(X)\Delta(X), the dispersion character of XX, is the minimum cardinality of a nonempty open subset of XX. Statements I and II are corollaries of the main result: for every regular space XX if X=Δ(X)|X|=\Delta(X) and every set AXA\subseteq X of cardinality cfX\mathrm{cf}|X| has a complete accumulation point, then XX is maximally resolvable. Moreover, regularity here can be weakened to π\pi-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}
}
R2 v1 2026-06-28T08:26:14.861Z