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Extensions of continuous functions: reflective functors

Published online by Cambridge University Press:  17 April 2009

W. N. Hunsaker  and
S. A. Naimpally
W. N. Hunsaker
Affiliation:
Department of Mathematics, Southern Illinois, University at Carbondale, Carbondale, Illinois 62901, United States of America
S. A. Naimpally
Affiliation:
Department of Mathematicsl Sciences, Lakehead University, Thunder Bay, Ontario, P7B 5E1, Canada.
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Abstract

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The purpose of this paper is to develop a general technique for attacking problems involving extensions of continuous functions from dense subspaces and to use it to obtain new results as well as to improve some of the known ones. The theory of structures developed by Harris is used to get some general results relating filters and covers. A necessary condition is derived for a continuous function f: X → Y to have a continuous extension : λx → λy where λZ denotes a given extension of the space Z. In the case of simple extensions, is continuous and in the case of strict extensions is θ-continuous. In the case of strict extensions, sufficient conditions for uniqueness of are derived. These results are then applied to several extensions considered by Banaschewski, Fomin, Kattov, Liu-Strecker, Blaszczyk-Mioduszewski, Rudölf, etc.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 35 , Issue 3 , June 1987 , pp. 455 - 470
Copyright
Copyright © Australian Mathematical Society 1987

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