Set of continuity points of functions with values in generalized metric spaces

L’ubica Holá; Zbigniew Piotrowski

doi:10.2478/v10127-009-0014-9

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Set of continuity points of functions with values in generalized metric spaces

Tatra Mountains Mathematical Publications

Volume 42 (2009): Issue 1 (April 2009)

By: L’ubica Holá and Zbigniew Piotrowski

Open Access

|Nov 2012

Abstract

We study continuity points of functions with values in generalized metric spaces. We define the generalized oscillation, which is a useful tool in our study. Let X be a topological space and Y be a weakly developable space. Let ƒ

: X →Y be a function. Then the set C (ƒ) of continuity points of ƒis a Gδ-set in X. Some results concerning continuity points of separately continuous functions as well as functions with closed graphs are also given.

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Articles in this issue

DOI: https://doi.org/10.2478/v10127-009-0014-9 | Journal eISSN: 1338-9750 | Journal ISSN: 12103195

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Language: English

Page range: 149 - 160

Published on: Nov 12, 2012

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

p-space,

Gδ-diagonal,

developable space,

weakly developable space,

quasicontinuous function,

generalized oscillation

Related subjects:

Mathematics,

General mathematics

© 2012 L’ubica Holá, Zbigniew Piotrowski, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons License.

Volume 42 (2009): Issue 1 (April 2009)