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On properties close to Polish cofinality in spaces of Baire-one and continuous functions

  • Alexander V. Osipov
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Abstract

In this paper we prove that B1(X) has a dense cofinally Polish subspace if and only if X is a Δ1-space. Also we prove that B1(X, [0,1]) has a dense cofinally Polish subspace if and only if X is a weak λ-space. We also establish that Cp(X, [0,1]) is pseudocompact if and only if Cp(X,[0,1]) has a dense cofinally Polish subspace. This result provides answers to four open questions from (Tkachuk in RACSAM 115(68), 2021).

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Cite

BibTeXRIS
BibTeX
@misc{osipov2026properties,
  title = {{On properties close to Polish cofinality in spaces of Baire-one and continuous functions}},
  author = {Alexander V. Osipov},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.04487},
  eprint = {2610.04487},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.04487},
}
RIS
TY  - UNPB
TI  - On properties close to Polish cofinality in spaces of Baire-one and continuous functions
AU  - Alexander V. Osipov
PY  - 2026
DA  - 2026/10/03
PB  - arXiv
DO  - 10.48550/arxiv.2610.04487
UR  - https://arxiv.org/abs/2610.04487
AB  - In this paper we prove that B_1(X) has a dense cofinally Polish subspace if and only if X is a Δ_1-space. Also we prove that B_1(X, [0,1]) has a dense cofinally Polish subspace if and only if X is a weak λ-space. We also establish that C_p(X, [0,1]) is pseudocompact if and only if C_p(X,[0,1]) has a dense cofinally Polish subspace. This result provides answers to four open questions from (Tkachuk in RACSAM 115(68), 2021).
ER  -