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International Journal of Mathematics and Mathematical Sciences
Volume 9, Issue 4, Pages 715-720

Characterizations of some near-continuous functions and near-open functions

Department of Mathematics, Indiana University Southeast, New Albany 47150, Indiana, USA

Received 7 April 1986

Copyright © 1986 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A subset N of a topological space is defined to be a θ-neighborhood of x if there exists an open set U such that xUC1UN. This concept is used to characterize the following types of functions: weakly continuous, θ-continuous, strongly θ-continuous, almost strongly θ-continuous, weakly δ-continuous, weakly open and almost open functions. Additional characterizations are given for weakly δ-continuous functions. The concept of θ-neighborhood is also used to define the following types of open maps: θ-open, strongly θ-open, almost strongly θ-open, and weakly δ-open functions.