Norm continuity of pointwise quasi-continuous mappings

Mirmostafaee, Alireza Kamel. "Norm continuity of pointwise quasi-continuous mappings." Mathematica Bohemica 143.3 (2018): 329-335. <http://eudml.org/doc/294853>.

@article{Mirmostafaee2018,
abstract = {Let $X$ be a Baire space, $Y$ be a compact Hausdorff space and $\varphi \colon X \rightarrow C_p(Y )$ 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 $X$.},
author = {Mirmostafaee, Alireza Kamel},
journal = {Mathematica Bohemica},
keywords = {function space; weak continuity; generalized continuity; quasi-continuous function; pointwise topology},
language = {eng},
number = {3},
pages = {329-335},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Norm continuity of pointwise quasi-continuous mappings},
url = {http://eudml.org/doc/294853},
volume = {143},
year = {2018},
}

TY - JOUR
AU - Mirmostafaee, Alireza Kamel
TI - Norm continuity of pointwise quasi-continuous mappings
JO - Mathematica Bohemica
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 143
IS - 3
SP - 329
EP - 335
AB - Let $X$ be a Baire space, $Y$ be a compact Hausdorff space and $\varphi \colon X \rightarrow C_p(Y )$ 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 $X$.
LA - eng
KW - function space; weak continuity; generalized continuity; quasi-continuous function; pointwise topology
UR - http://eudml.org/doc/294853
ER -