CLASSIFICATION OF POINTS OF SEMI-CONTINUITY AND SEMI-DISCONTINUITY OF A MAPPING IN TOPOLOGICAL SPACES

摘要

In this paper we point out a distinction between a point of semi-continuity in global sense and a point of semi-continuity in local sense in general topological spaces after classifying points of semi-continuity and semi-discontinuity and also their interrclationships. In particular, we find a sufficient condition for a bijective open map on a Hausdorff space to be semi-continuous. Furthermore, behaviour of semi-discontinuous functions which closely resemble with semi-continuous functions somewhere are scrutinized and discussed when the range space is compact and Hausdorff. Finally, a sufficient condition for an open bijection on the real line to have at most countable points of discontinuity is formulated.