A study of near continuous function spaces

Abstract

Even though continuous function has been intensively studied in general topology, near continuous function, for instance, almost continuous function, connected function, etc., could be used to introduce the important property of continuity, In this paper, special non-continuous functions are introduced. One observes the properties which is related with continuity and tries to introduce weaker topologies to fit these near continuous function spaces. It is well known that uniform convergence is equivalent to compact open topology in C[a,b] = the set of all continuous functions defined on [a,b] and graph topology is effectively used to clarify the relation. One uses the method of graph topology to investigate the relations of various function spaces. In particular, partially ordered relation, separation axiom, and closure of the set of functions are intensively studied. As the main result of this study, non continuous function space could be systematically generalized in topological space, In this paper, unless it is clearly mentioned, all notations and definitions are the same with Kelley's "General Topology".;본 논문에서는 먼저 특수한 성질을 지니고 있는 비연속함수를 조사하고, 연속성과 관련된 성질들을 연구하여, 이러한 비연속함수에 적합한 위상구조를 소개하였다. 특히 이러한 위상구조들의 준순서, 분리공리, 폐포(closure)에 대해 연구하였다.