| Title:
|
A characterization of almost continuity and weak continuity (English) |
| Author:
|
Petalas, Chrisostomos |
| Author:
|
Vidalis, Theodoros |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
43 |
| Issue:
|
1 |
| Year:
|
2004 |
| Pages:
|
133-136 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is well known that a function $f$ from a space $X$ into a space $Y$ is continuous if and only if, for every set $K$ in $X$ the image of the closure of $K$ under $f$ is a subset of the closure of the image of it. In this paper we characterize almost continuity and weak continuity by proving similar relations for the subsets $K$ of $X$. (English) |
| Keyword:
|
almost continuous function |
| Keyword:
|
weakly continuous function |
| MSC:
|
54C08 |
| MSC:
|
54C10 |
| idZBL:
|
Zbl 1064.54025 |
| idMR:
|
MR2124610 |
| . |
| Date available:
|
2009-08-21T12:54:55Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/132944 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Long P. E., McGehee E. E.: Properties of almost continuous functions.Proc. Amer. Math. Soc. 24 (1970), 175–180. Zbl 0186.56003, MR 0251704 |
| Reference:
|
[4] Long P. E., Carnahan D. A.: Comparing almost continuous functions.Proc. Amer. Math. Soc. 38 (1973), 413–418. Zbl 0261.54007, MR 0310824 |
| Reference:
|
[5] Noire T. : On weakly continuous mappings.Proc. Amer. Math. Soc. 46 (1974), 120–124. MR 0348698 |
| Reference:
|
[6] Saleh M.: Almost continuity implies closure continuity.Glaskow Math. J. 40 (1998), 263–264. Zbl 0898.54015, MR 1630179 |
| Reference:
|
[7] Singal M. K., Singal A. R.: Almost continuous mappings.Yokohama Math. J. 16 (1968), 63–73. Zbl 0191.20802, MR 0261569 |
| . |
