D-Continuity

Authors

DOI:

https://doi.org/10.37256/cm.5420245273

Keywords:

topological spaces, real-valued functions, subspaces, compactness, local compactness, continuous maps

Abstract

We call a map f : X Y D-continuous if its restriction to any set of points that do not possess compact neighborhoods is continuous. We investigate this weaker version of continuity and provide examples to compare D-continuity with other types of continuity. Let f : X Y be a D-continuous bijective map such that f(A) is locally finite, where A is the set of all points that do not possess compact neighborhoods in X. Then, we show that f|A is a homeomorphism. We also show that if X is a countably generated topological space, then any D-continuous f : X is continuous. We discuss C-normality, illustrating the relationship between this property and D-continuity. Finally, we investigate the space of all real-valued D-continuous maps of an arbitrary topological space X and obtain some results.

Downloads

Published

2024-11-20

How to Cite

1.
Zailai M. <i>D</i>-Continuity. Contemp. Math. [Internet]. 2024 Nov. 20 [cited 2024 Dec. 4];5(4):5231-7. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/5273

Issue

Section

Research Article

Categories