| Title:
|
Norm continuity of pointwise quasi-continuous mappings (English) |
| Author:
|
Mirmostafaee, Alireza Kamel |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
143 |
| Issue:
|
3 |
| Year:
|
2018 |
| Pages:
|
329-335 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $X$ be a Baire space, $Y$ be a compact Hausdorff space and $\varphi \colon X \to C_p(Y )$ 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 $X$. (English) |
| Keyword:
|
function space |
| Keyword:
|
weak continuity |
| Keyword:
|
generalized continuity |
| Keyword:
|
quasi-continuous function |
| Keyword:
|
pointwise topology |
| MSC:
|
54C05 |
| MSC:
|
54C08 |
| MSC:
|
54C35 |
| idZBL:
|
Zbl 06940886 |
| idMR:
|
MR3852297 |
| DOI:
|
10.21136/MB.2018.0016-17 |
| . |
| Date available:
|
2018-08-31T09:44:55Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147391 |
| . |
| Reference:
|
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| . |
