Home > Iowa Academy of Science > Journals & Newsletters > Proceedings of the Iowa Academy of Science > Volume 60 (1953) > Annual Issue
Document Type
Research
Abstract
Let X be a Hausdorff space in which each neighborhood an inexhaustible set (a set of Baire's second category), and let {N} denote the system of neighborhoods in X. Thus N (x) is a neighborhood of the element x. Let Y be a regular separable Hausdorff space and let {M} denote the system of neighborhoods in Y. If f is a function on X into Y and ξ is a point of X, then f is continuous at ξ if for every M(f(ξ)) and for every N(ξ), the set N(ξ) E[x:f (x) εM (f (ξ))] contains ξ as an interior point. A direct method for generalizing continuity is to weaken the requirements on the set N(ξ)E[x:f(x)εM(f(ξ)) ].
Publication Date
1953
Journal Title
Proceedings of the Iowa Academy of Science
Volume
60
Issue
1
First Page
477
Last Page
481
Copyright
©1953 Iowa Academy of Science, Inc.
Language
en
File Format
application/pdf
Recommended Citation
Cargal, Buchanan
(1953)
"Generalizations of Continuity,"
Proceedings of the Iowa Academy of Science, 60(1), 477-481.
Available at:
https://scholarworks.uni.edu/pias/vol60/iss1/60