Continuous images and other topological properties of Valdivia compacta

Ondřej Kalenda

Fundamenta Mathematicae (1999)

  • Volume: 162, Issue: 2, page 181-192
  • ISSN: 0016-2736

Abstract

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We study topological properties of Valdivia compact spaces. We prove in particular that a compact Hausdorff space K is Corson provided each continuous image of K is a Valdivia compactum. This answers a question of M. Valdivia (1997). We also prove that the class of Valdivia compacta is stable with respect to arbitrary products and we give a generalization of the fact that Corson compacta are angelic.

How to cite

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Kalenda, Ondřej. "Continuous images and other topological properties of Valdivia compacta." Fundamenta Mathematicae 162.2 (1999): 181-192. <http://eudml.org/doc/212418>.

@article{Kalenda1999,
abstract = {We study topological properties of Valdivia compact spaces. We prove in particular that a compact Hausdorff space K is Corson provided each continuous image of K is a Valdivia compactum. This answers a question of M. Valdivia (1997). We also prove that the class of Valdivia compacta is stable with respect to arbitrary products and we give a generalization of the fact that Corson compacta are angelic.},
author = {Kalenda, Ondřej},
journal = {Fundamenta Mathematicae},
keywords = {Corson compact space; Valdivia compact space; countably compact space; Fréchet-Urysohn space; continuous image; countably compact; Fréchet-Uryson space; Valdivia compactness; Corson compact; Corson compactness; Valdivia compactum; Corson compactum},
language = {eng},
number = {2},
pages = {181-192},
title = {Continuous images and other topological properties of Valdivia compacta},
url = {http://eudml.org/doc/212418},
volume = {162},
year = {1999},
}

TY - JOUR
AU - Kalenda, Ondřej
TI - Continuous images and other topological properties of Valdivia compacta
JO - Fundamenta Mathematicae
PY - 1999
VL - 162
IS - 2
SP - 181
EP - 192
AB - We study topological properties of Valdivia compact spaces. We prove in particular that a compact Hausdorff space K is Corson provided each continuous image of K is a Valdivia compactum. This answers a question of M. Valdivia (1997). We also prove that the class of Valdivia compacta is stable with respect to arbitrary products and we give a generalization of the fact that Corson compacta are angelic.
LA - eng
KW - Corson compact space; Valdivia compact space; countably compact space; Fréchet-Urysohn space; continuous image; countably compact; Fréchet-Uryson space; Valdivia compactness; Corson compact; Corson compactness; Valdivia compactum; Corson compactum
UR - http://eudml.org/doc/212418
ER -

References

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  1. [A] A. V. Arkhangel'skiĭ, Topological Spaces of Functions, Moscow State Univ., 1989 (in Russian); English transl.: Kluwer Acad. Publ., Dordrecht, 1992. 
  2. [AMN] S. Argyros, S. Mercourakis and S. Negrepontis, Functional-analytic properties of Corson-compact spaces, Studia Math. 89 (1988), 197-229. Zbl0656.46014
  3. [C] H. H. Corson, Normality in subsets of product spaces, Amer. J. Math. 81 (1959), 785-796. Zbl0095.37302
  4. [DG] R. Deville and G. Godefroy, Some applications of projective resolutions of identity, Proc. London Math. Soc. 67 (1993), 183-199. Zbl0798.46008
  5. [FGZ] M. Fabian, G. Godefroy and V. Zizler, A note on Asplund generated Banach spaces, Bull. Polish Acad. Sci. Math. 47 (1999), 221-230. 
  6. [G] I. Glicksberg, Stone-Čech compactifications of products, Trans. Amer. Math. Soc. 90 (1959), 369-382. Zbl0089.38702
  7. [K1] O. Kalenda, An example concerning Valdivia compact spaces, Serdica Math. J. 25 (1999), 131-140. Zbl0946.46020
  8. [K2] O. Kalenda, A characterization of Valdivia compact spaces, Collect. Math., to appear. Zbl0949.46004
  9. [K3] O. Kalenda, Valdivia compacta and equivalent norms, preprint KMA-1999-02, Charles University, Prague. 
  10. [V1] M. Valdivia, Projective resolutions of the identity in C(K) spaces, Arch. Math. (Basel) 54 (1990), 493-498. Zbl0707.46009
  11. [V2] M. Valdivia, Simultaneous resolutions of the identity operator in normed spaces, Collect. Math. 42 (1991), 265-285. Zbl0788.47024
  12. [V3] M. Valdivia, On certain compact topological spaces, Rev. Mat. Univ. Complut. Madrid 10 (1997), 81-84. Zbl0870.54025

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