Points of continuity of quasi-continuous functions

In: Tatra Mountains Mathematical Publications, vol. 76, no. 2

Marzieh Neghaban - Alireza Kamel Mirmostafaee

Details:

Year, pages: 2020, 53 - 62

Keywords:

joint continuity, separate continuity, quasi-continuity, closed graph.

Article type: Mathematics - Real Functions

Document type: Scientific paper

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

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About article:

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 $wΔ$-spaces is a $G_δ$ subset of its domain provided that its domain is a $W$-space.

How to cite:

ISO 690:

Neghaban, M., Mirmostafaee, A. 2020. Points of continuity of quasi-continuous functions. In Tatra Mountains Mathematical Publications, vol. 76, no.2, pp. 53-62. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2020-0017

APA:

Neghaban, M., Mirmostafaee, A. (2020). Points of continuity of quasi-continuous functions. Tatra Mountains Mathematical Publications, 76(2), 53-62. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2020-0017

About edition:

Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava

Published: 20. 10. 2020

Rights:

The Creative Commons Attribution-NC-ND 4.0 International Public License