Mathematica Bohemica, Volume (143), No (2), Year (2018-1) , Pages (1-7)

#### Title : ( Norm continuity of pointwise quasi-continuous mappings into function spaces )

Authors: Seyyed Alireza Kamel Mirmostafaee ,

Citation: BibTeX | EndNote

#### Abstract

Let $X$ be a Baire space, $Y$ be a compact Hausdorff space and $\varphi:X \to C_p(Y )$ be a quasi-continuous mapping. For a proximal subset $H$ of $Y \times Y$, we will use topological games $\mathcal{G}_1(H)$ and $\mathcal{G}_2(H)$ on $Y \times Y$ between two players to prove that if the first player has a winning strategy in these games, then $\varphi$ is norm-continuous on a dense $G_\delta$ subset of $X$. It follows that if $Y$ is Valdivia compact, each quasi-continuous mapping from a Baire space $X$ to $C_p(Y)$ is norm continuous on a dense $G_\delta$ subset of $X$.

#### Keywords

, Function space, weak and generalized continuity, quasi-continuous function, pointwise topology.
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@article{paperid:1065718,
author = {Kamel Mirmostafaee, Seyyed Alireza},
title = {Norm continuity of pointwise quasi-continuous mappings into function spaces},
journal = {Mathematica Bohemica},
year = {2018},
volume = {143},
number = {2},
month = {January},
issn = {0862-7959},
pages = {1--7},
numpages = {6},
keywords = {Function space;weak and generalized continuity; quasi-continuous function; pointwise topology.},
}