<abstract xmlns="http://www.w3.org/1999/xhtml"><p>We study points of joint continuity of multi-variable separately quasi-continuous functions which are continuous with respect to one variable. We will show that the assumption of complete regularity in the paper of V. Maslyuchenko et al in ”Tatra Mt. Math. Pub. 68, (2017), 47–58” can be removed in some situations. Moreover, we use a topological game argument to prove that the set of points of continuity of functions with closed graph into <italic>ω</italic>Δ-spaces is a <italic>G<sub>δ</sub></italic> subset of its domain provided that its domain is a <italic>W</italic>-space.</p></abstract>

We study points of joint continuity of multi-variable separately quasi-continuous functions which are continuous with respect to one variable. We will show that the assumption of complete regularity in the paper of V. Maslyuchenko et al in ”Tatra Mt. Math. Pub. 68, (2017), 47–58” can be removed in some situations. Moreover, we use a topological game argument to prove that the set of points of continuity of functions with closed graph into ωΔ-spaces is a Gδ subset of its domain provided that its domain is a W-space.

Points of Continuity of Quasi-Continuous Functions

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Points of Continuity of Quasi-Continuous Functions"}

We study points of joint continuity of multi-variable separately quasi-continuous functions which are continuous with respect to one variable. We will show...

Points of Continuity of Quasi-Continuous Functions

Published Online: Nov 04, 2020

Page range: 53 - 62

Received: Jul 08, 2019

DOI: https://doi.org/10.2478/tmmp-2020-0017

Keywords
Joint continuity, separate continuity, quasi-continuity, closed graph

© 2020 Marzieh Neghaban et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Points of Continuity of Quasi-Continuous Functions

Published Online: Nov 04, 2020

Page range: 53 - 62

Received: Jul 08, 2019

DOI: https://doi.org/10.2478/tmmp-2020-0017

KeywordsJoint continuity, separate continuity, quasi-continuity, closed graph

© 2020 Marzieh Neghaban et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Joint continuity, separate continuity, quasi-continuity, closed graph