Continuous images and other topological properties of Valdivia compacta

• Autorzy: Ondřej Kalenda
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Corson compact space; Valdivia compact space; countably compact space; Fréchet-Urysohn space; continuous image

Kategorie tematyczne

• 54D30: Compactness
• 54C05: Continuous maps

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1999
• Tom: 162
• Numer: 2
• Strony: 181-192

Daty

wydano

1999

otrzymano

1998-08-05

poprawiono

1999-03-26

Twórcy

autor

Ondřej Kalenda

• Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic

Bibliografia

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