Semimetric spaces: topological considerations

João Ferreira do Amaral

No 2020/0117, Working Papers REM from ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa

Abstract: In a previous paper (Amaral 2007) we introduced several issues related to the definition of convexity in semimetric spaces that is, spaces (E,d) such that E is a fundamental set and d is a real function d: E x E?R that satisfies all the conditions of a metric excluding the triangular inequality. In that paper we explicitly postponed to a future paper the discussion on the possibilities of defining a significant topology for a semimetric space. The aim of the present paper is to discuss this issue. In section 1 we mention already known results or results easily derived from known ones. In section 2 we used these results to obtain a sufficient condition to define a topology on a semimetric space.

Date: 2020-03
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