Points of Upper and Lower Semicontinuity for Multivalued Functions

Mirmostafaee, Alireza Kamel

doi:10.1007/s11253-018-1441-z

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Marzieh Neghaban -Alireza Kamel Mirmostafaee1

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2020

2022

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“…A function f : X × Y → Z is called a KC-function if it is quasi-continuous with respect to the first variable and continuous with respect to the second variable. A few mathematicians studied points of joint continuity of KC-functions see, e.g., [3,6,10,16,17,20,22,23] and the survey paper of Neubrunn [25]). In particular, Piotrowski [26] proved the following result.…”

Section: Marzieh Neghaban -Alireza Kamel Mirmostafaeementioning

confidence: 99%

Points of Continuity of Quasi-Continuous Functions

Neghaban

Mirmostafaee

2020

Tatra Mountains Mathematical Publications

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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.

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