Embedding of the ordinal segment [ 0 , ω 1 ] into continuous images of Valdivia compacta

Ondřej F. K. Kalenda

Commentationes Mathematicae Universitatis Carolinae (1999)

  • Volume: 40, Issue: 4, page 777-783
  • ISSN: 0010-2628

Abstract

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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 , ω 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.

How to cite

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Kalenda, Ondřej F. K.. "Embedding of the ordinal segment $[0,\omega _1]$ into continuous images of Valdivia compacta." Commentationes Mathematicae Universitatis Carolinae 40.4 (1999): 777-783. <http://eudml.org/doc/248429>.

@article{Kalenda1999,
abstract = {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.},
author = {Kalenda, Ondřej F. K.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Corson compact space; Valdivia compact space; continuous image; ordinal segment; Corson compact space; Valdivia compact space; continuous image; ordinal segment},
language = {eng},
number = {4},
pages = {777-783},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Embedding of the ordinal segment $[0,\omega _1]$ into continuous images of Valdivia compacta},
url = {http://eudml.org/doc/248429},
volume = {40},
year = {1999},
}

TY - JOUR
AU - Kalenda, Ondřej F. K.
TI - Embedding of the ordinal segment $[0,\omega _1]$ into continuous images of Valdivia compacta
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 4
SP - 777
EP - 783
AB - 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.
LA - eng
KW - Corson compact space; Valdivia compact space; continuous image; ordinal segment; Corson compact space; Valdivia compact space; continuous image; ordinal segment
UR - http://eudml.org/doc/248429
ER -

References

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  1. Some applications of projective resolutions of identity, Proc. London Math. Soc. 67 1 (1993), 183-199. (1993) Zbl0798.46008MR1218125
  2. Fabian M., Gâteaux differentiability of convex functions and topology: weak Asplund spaces, Wiley-Interscience, New York (1997), 180. (1997) Zbl0883.46011MR1461271
  3. Fabian M., Godefroy G., Zizler V., A note on Asplund generated Banach spaces, Bull. Acad. Polon. Sci. 47 2 (1999 to appear). (1999 to appear) Zbl0946.46016MR1711819
  4. Godefroy G., Talagrand M., Espaces de Banach représentables, Israel J. Math. 41 4 (1982), 321-330. (1982) Zbl0498.46016MR0657864
  5. Gul'ko S.P., Properties of sets that lie in Σ -products (in Russian), Dokl. Akad. Nauk SSSR 237 (1977), 3 505-508. (1977) MR0461410
  6. Kalenda O., Stegall compact spaces which are not fragmentable, Topology Appl. 96 2 (1999), 121-132. (1999) Zbl0991.54030MR1702306
  7. Kalenda O., Continuous images and other topological properties of Valdivia compacta, Fund. Math., to appear. Zbl0989.54019MR1734916
  8. Kalenda O., A characterization of Valdivia compact spaces, Collectanea Math., to appear. Zbl0949.46004MR1757850
  9. Kalenda O., Valdivia compacta and equivalent norms, preprint. Zbl1073.46009MR1749079
  10. Kalenda O., Valdivia compacta and subspaces of C ( K ) spaces, preprint KMA-1999-02, Charles University, Prague. Zbl0983.46020MR1759476
  11. Noble N., The continuity of functions on Cartesian products, Trans. Amer. Math. Soc. 149 (1970), 187-198. (1970) Zbl0229.54028MR0257987
  12. Valdivia M., Projective resolutions of the identity in C ( K ) spaces, Archiv der Math. 54 (1990), 493-498. (1990) MR1049205
  13. Valdivia M., Simultaneous resolutions of the identity operator in normed spaces, Collectanea Math. 42 3 (1991), 265-285. (1991) Zbl0788.47024MR1203185
  14. Valdivia M., On certain compact topological spaces, Revista Matemática de la Universidad Complutense de Madrid 10 1 (1997), 81-84. (1997) Zbl0870.54025MR1452564

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