54E05 Proximity structures and generalizations
54E15 Uniform structures and generalizations
54E17 Nearness spaces
54E18 $p$-spaces, $M$-spaces, $\sigma$-spaces, etc.
54E20 Stratifiable spaces, cosmic spaces, etc.
54E25 Semimetric spaces
54E30 Moore spaces
54E35 Metric spaces, metrizability
54E40 Special maps on metric spaces
54E45 Compact (locally compact) metric spaces
54E50 Complete metric spaces
54E52 Baire category, Baire spaces
54E55 Bitopologies
54E70 Probabilistic metric spaces
54E99 None of the above, but in this section