On symmetrizability and perfectness of second-countable spaces
Abstract
A symmetrizability criterion of Arhangelskii implies that a second-countable Hausdorff space is symmetrizable if and only if it is perfect. We present an example of a non-symmetrizable second-countable submetrizable space of cardinality $\mathfrak q_0$ and study the smallest possible cardinality $\mathfrak q_i$ of a non-symmetrizable second-countable $T_i$-space for $i\in\{1,2\}$.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2022
- DOI:
- 10.48550/arXiv.2206.01671
- arXiv:
- arXiv:2206.01671
- Bibcode:
- 2022arXiv220601671B
- Keywords:
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- Mathematics - General Topology;
- 54A35;
- 54E35;
- 54H05
- E-Print:
- 4 pages