Inspired by the fact that a compact topological group is hereditarily normal if and only if it is metrizable, we prove that various levels of compactness-like properties imposed on a topological group G allow one to establish that G is hereditarily normal if and only if G is metrizable (among these properties are locally compactness, local minimality and \omega-boundedness). This extends recent results from [4] in the case of countable compactness.
Metrizability of some hereditarily normal compact like groups
DIKRANJAN, Dikran;IMPIERI, Daniele;TOLLER, Daniele
2013-01-01
Abstract
Inspired by the fact that a compact topological group is hereditarily normal if and only if it is metrizable, we prove that various levels of compactness-like properties imposed on a topological group G allow one to establish that G is hereditarily normal if and only if G is metrizable (among these properties are locally compactness, local minimality and \omega-boundedness). This extends recent results from [4] in the case of countable compactness.File in questo prodotto:
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