| Title:
|
Embedding of the ordinal segment $[0,\omega_1]$ into continuous images of Valdivia compacta (English) |
| Author:
|
Kalenda, Ondřej |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
40 |
| Issue:
|
4 |
| Year:
|
1999 |
| Pages:
|
777-783 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove in particular that a continuous image of a Valdivia compact space is Corson provided it contains no homeomorphic copy of the ordinal segment $[0,\omega_1]$. This generalizes a result of R. Deville and G. Godefroy who proved it for Valdivia compact spaces. We give also a refinement of their result which yields a pointwise version of retractions on a Valdivia compact space. (English) |
| Keyword:
|
Corson compact space |
| Keyword:
|
Valdivia compact space |
| Keyword:
|
continuous image |
| Keyword:
|
ordinal segment |
| MSC:
|
54C05 |
| MSC:
|
54D30 |
| idZBL:
|
Zbl 1009.54017 |
| idMR:
|
MR1756552 |
| . |
| Date available:
|
2009-01-08T18:57:25Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119130 |
| . |
| Reference:
|
: Some applications of projective resolutions of identity.Proc. London Math. Soc. 67 1 (1993), 183-199. Zbl 0798.46008, MR 1218125 |
| Reference:
|
Fabian M.: Gâteaux differentiability of convex functions and topology: weak Asplund spaces.Wiley-Interscience, New York (1997), 180. Zbl 0883.46011, MR 1461271 |
| Reference:
|
Fabian M., Godefroy G., Zizler V.: A note on Asplund generated Banach spaces.Bull. Acad. Polon. Sci. 47 2 (1999 \toappear). Zbl 0946.46016, MR 1711819 |
| Reference:
|
Godefroy G., Talagrand M.: Espaces de Banach représentables.Israel J. Math. 41 4 (1982), 321-330. Zbl 0498.46016, MR 0657864 |
| Reference:
|
Gul'ko S.P.: Properties of sets that lie in $\Sigma $-products (in Russian).Dokl. Akad. Nauk SSSR 237 (1977), 3 505-508. MR 0461410 |
| Reference:
|
Kalenda O.: Stegall compact spaces which are not fragmentable.Topology Appl. 96 2 (1999), 121-132. Zbl 0991.54030, MR 1702306 |
| Reference:
|
Kalenda O.: Continuous images and other topological properties of Valdivia compacta.Fund. Math., to appear. Zbl 0989.54019, MR 1734916 |
| Reference:
|
Kalenda O.: A characterization of Valdivia compact spaces.Collectanea Math., to appear. Zbl 0949.46004, MR 1757850 |
| Reference:
|
Kalenda O.: Valdivia compacta and equivalent norms.preprint. Zbl 1073.46009, MR 1749079 |
| Reference:
|
Kalenda O.: Valdivia compacta and subspaces of $C(K)$ spaces.preprint KMA-1999-02, Charles University, Prague. Zbl 0983.46020, MR 1759476 |
| Reference:
|
Noble N.: The continuity of functions on Cartesian products.Trans. Amer. Math. Soc. 149 (1970), 187-198. Zbl 0229.54028, MR 0257987 |
| Reference:
|
Valdivia M.: Projective resolutions of the identity in $C(K)$ spaces.Archiv der Math. 54 (1990), 493-498. MR 1049205 |
| Reference:
|
Valdivia M.: Simultaneous resolutions of the identity operator in normed spaces.Collectanea Math. 42 3 (1991), 265-285. Zbl 0788.47024, MR 1203185 |
| Reference:
|
Valdivia M.: On certain compact topological spaces.Revista Matemática de la Universidad Complutense de Madrid 10 1 (1997), 81-84. Zbl 0870.54025, MR 1452564 |
| . |
