| Title:
|
Analytic functions are $\Cal I$-density continuous (English) |
| Author:
|
Ciesielski, Krzysztof |
| Author:
|
Larson, Lee |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
35 |
| Issue:
|
4 |
| Year:
|
1994 |
| Pages:
|
645-652 |
| . |
| Category:
|
math |
| . |
| Summary:
|
A real function is $\Cal I$-density continuous if it is continuous with the $\Cal I$-density topology on both the domain and the range. If $f$ is analytic, then $f$ is $\Cal I$-density continuous. There exists a function which is both $C^\infty $ and convex which is not $\Cal I$-density continuous. (English) |
| Keyword:
|
analytic function |
| Keyword:
|
$\Cal I$-density continuous |
| Keyword:
|
$\Cal I$-density topology |
| MSC:
|
26A21 |
| MSC:
|
26E05 |
| MSC:
|
26E10 |
| idZBL:
|
Zbl 0826.26011 |
| idMR:
|
MR1321235 |
| . |
| Date available:
|
2009-01-08T18:14:05Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118706 |
| . |
| Reference:
|
[1] Aversa V., Wilczyński W.: Homeomorphisms preserving $\Cal I$-density points.Boll. Un. Mat. Ital. B(7)1 (1987), 275-285. MR 0895464 |
| Reference:
|
[2] Ciesielski K., Larson L.: The space of density continuous functions.Acta Math. Hung. 58 (1991), 289-296. Zbl 0757.26006, MR 1153484 |
| Reference:
|
[3] Poreda W., Wagner-Bojakowska E., Wilczyński W.: A category analogue of the density topology.Fund. Math. 75 (1985), 167-173. MR 0813753 |
| Reference:
|
[4] Wilczyński W.: A generalization of the density topology.Real Anal. Exchange 8(1) (1982-83), 16-20. |
| Reference:
|
[5] Wilczyński W.: A category analogue of the density topology, approximate continuity, and the approximate derivative.Real Anal. Exchange 10 (1984-85), 241-265. MR 0790803 |
| . |
