Seminormal functors and paranormality. (English. Russian original) Zbl 1518.54006
Mosc. Univ. Math. Bull. 78, No. 2, 100-104 (2023); translation from Vestn. Mosk. Univ., Ser. I 78, No. 2, 67-71 (2023).
Summary: It is known that if a space \(\mathcal{F}(X)\) is hereditarily paranormal for a paracompact \(p\)-space \(X\) and normal functor \(\mathcal{F}\) of degree \(\geqslant 3\) in the category \(\mathcal{P}\) of paracompact \(p\)-spaces and their perfect maps, then \(X\) is metrizable [A. P. Kombarov, Mosc. Univ. Math. Bull. 72, No. 5, 203–205 (2017; Zbl 1383.54024); translation from Vestn. Mosk. Univ., Ser. I 72, No. 5, 48–51 (2017)]. In this paper, a generalization of this theorem is proved for seminormal functors in the category \(\mathcal{P} \).
MSC:
| 54B30 | Categorical methods in general topology |
| 54D20 | Noncompact covering properties (paracompact, Lindelöf, etc.) |
| 54E35 | Metric spaces, metrizability |
Citations:
Zbl 1383.54024References:
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