DEGREE OF NEARNESS

Abstract

This paper is a revised version of [5]. In [5], we define 'nearness between two points' in a topological space in many ways and show that a continuous function preserves one-sided nearness. We also show that a T1-space is characterized by one-sided nearness exactly. In this paper, we introduce extremally disconnected spaces and show that the new topology generated by the set of equivalence classes as a base is extremally disconnected.

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