# Article

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Keywords:
Corson compact space; Valdivia compact space; continuous image; ordinal segment
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.
References:
Some applications of projective resolutions of identity. Proc. London Math. Soc. 67 1 (1993), 183-199. MR 1218125 | Zbl 0798.46008
Fabian M.: Gâteaux differentiability of convex functions and topology: weak Asplund spaces. Wiley-Interscience, New York (1997), 180. MR 1461271 | Zbl 0883.46011
Fabian M., Godefroy G., Zizler V.: A note on Asplund generated Banach spaces. Bull. Acad. Polon. Sci. 47 2 (1999 \toappear). MR 1711819 | Zbl 0946.46016
Godefroy G., Talagrand M.: Espaces de Banach représentables. Israel J. Math. 41 4 (1982), 321-330. MR 0657864 | Zbl 0498.46016
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
Kalenda O.: Stegall compact spaces which are not fragmentable. Topology Appl. 96 2 (1999), 121-132. MR 1702306 | Zbl 0991.54030
Kalenda O.: Continuous images and other topological properties of Valdivia compacta. Fund. Math., to appear. MR 1734916 | Zbl 0989.54019
Kalenda O.: A characterization of Valdivia compact spaces. Collectanea Math., to appear. MR 1757850 | Zbl 0949.46004
Kalenda O.: Valdivia compacta and equivalent norms. preprint. MR 1749079 | Zbl 1073.46009
Kalenda O.: Valdivia compacta and subspaces of $C(K)$ spaces. preprint KMA-1999-02, Charles University, Prague. MR 1759476 | Zbl 0983.46020
Noble N.: The continuity of functions on Cartesian products. Trans. Amer. Math. Soc. 149 (1970), 187-198. MR 0257987 | Zbl 0229.54028
Valdivia M.: Projective resolutions of the identity in $C(K)$ spaces. Archiv der Math. 54 (1990), 493-498. MR 1049205
Valdivia M.: Simultaneous resolutions of the identity operator in normed spaces. Collectanea Math. 42 3 (1991), 265-285. MR 1203185 | Zbl 0788.47024
Valdivia M.: On certain compact topological spaces. Revista Matemática de la Universidad Complutense de Madrid 10 1 (1997), 81-84. MR 1452564 | Zbl 0870.54025

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