Semimetrics, semiécarts in ordered semigroups
Semimetrizable, Summetrizable And Sizable Spaces.
Sequential characterizations of metrizability
Über Distanzfunktionen mit Werten in angeordneten Halbgruppen.
Weak-bases and -spaces
It is shown that certain weak-base structures on a topological space give a -space. This solves the question by A.V. Arhangel’skii of when quotient images of metric spaces are -spaces. A related result about symmetrizable spaces also answers a question of Arhangel’skii. Theorem.Any symmetrizable space is a -space hereditarily. Hence, quotient mappings, with compact fibers, from metric spaces have a -space image. What about quotient -mappings? Arhangel’skii and Buzyakova have shown that...
Weakly complete semimetrizable spaces and complete metrizability.
In [4], J. Ceder proved that every paracompact strongly complete semimetrizable space is completely metrizable. This result cannot be generalized to paracompact weakly complete semimetrizable spaces as a known example of L. F. McAuley shows (see [11, Theorem 3.2]). It then arises, in a natural way, the question of obtaining conditions for the complete metrizability of a paracompact weakly complete semimetrizable space. In this note we give an answer to this question. We show that every regular theta,...