Functions weaker than continuous functions

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Willie Carter High (Creator)
The University of North Carolina at Greensboro (UNCG )
Web Site:
Hughes Hoyle

Abstract: Many properties which are characteristic of continuous function remain valid for several classes of non-continuous functions if appropriate limitations are imposed. Some problems of topology may be solved only through the study of non-continuous functions. In particular, Almost-Continuous Mappings by Singal and Singal [2] turn out to be the natural tool for studying almost-compact spaces (A space is said to be almost-compact if each open cover has a finite subfamily whose closures cover the space) of Alexandroff and Urysohn and also nearly-compact spaces (A space is said to be nearly-compact if every open cover has a finite subfamily the interiors of the closures of whose members cover the space) in as much as every almost-continuous image of an almost-compact space is almost-compact and every almost-continuous open image of a nearly-compact space is nearly-compact [3]. One of the aims of this thesis is to define some functions weaker than continuous functions in a topological space and to study the compositions, restrictions and extensions of these functions which are closely parallel to the elementary properties of continuous functions. The ideas behind these results originated in [1], [2] and [6].

Additional Information

Language: English
Date: 1972
Functions, Continuous
Topological spaces
Mappings (Mathematics)

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