On symmetrizability and perfectness of second-countable spaces
Keywords:
symmetrizable space, submetrizable space, $Q$-space, cardinal characteristic of the continuumAbstract
A symmetrizability criterion of Arhangelskǐ 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 $q_0$ and study the smallest possible cardinality $q_i$ of a non-symmetrizable secondcountable $T_i$-space for $i \in\{1,2\}$.
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