•  
  •  
 

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

© Copyright 1953 by the Iowa Academy of Science, Inc.

Language

EN

File Format

application/pdf

Share

COinS