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PreprintCC BY 4.0arXiv

Countable compactness is A-invariant

  • ZhouXiang Huang
Open at sourcePDFDOICite

Abstract

Let A(X) denote the free Abelian topological group over a Tychonoff space X. We prove that if A(X) and A(Y) are topologically isomorphic and X is countably compact, then Y is also countably compact. Thus countable compactness is an A-invariant and, consequently, an M-invariant; this answers Open Problem~7.10.1 of Arhangel'skii and Tkachenko.

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Cite

BibTeXRIS
BibTeX
@misc{huang2026countable,
  title = {{Countable compactness is $A$-invariant}},
  author = {ZhouXiang Huang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.12131},
  eprint = {2610.12131},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.12131},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Countable compactness is A-invariant
AU  - ZhouXiang Huang
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.12131
UR  - https://arxiv.org/abs/2610.12131
AB  - Let A(X) denote the free Abelian topological group over a Tychonoff space X. We prove that if A(X) and A(Y) are topologically isomorphic and X is countably compact, then Y is also countably compact. Thus countable compactness is an A-invariant and, consequently, an M-invariant; this answers Open Problem~7.10.1 of Arhangel'skii and Tkachenko.
ER  -