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Only 3-generalized metric spaces have a compatible symmetric topology. (English) Zbl 1348.54025

Summary: We prove that every 3-generalized metric space is metrizable. We also show that for any \(v\) with \(v\geq 4\), not every \(v\)-generalized metric space has a compatible symmetric topology.

MSC:

54E99 Topological spaces with richer structures
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