The compact extension property: the role of compactness

Jos Bijl; Jan van Mill

Commentationes Mathematicae Universitatis Carolinae (1991)

  • Volume: 32, Issue: 2, page 369-375
  • ISSN: 0010-2628

Abstract

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We consider separable metrizable topological spaces. Among other things we prove that there exists a non-contractible space with the compact extension property and we prove a new version of realization of polytopes for ANR ’s.

How to cite

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Bijl, Jos, and van Mill, Jan. "The compact extension property: the role of compactness." Commentationes Mathematicae Universitatis Carolinae 32.2 (1991): 369-375. <http://eudml.org/doc/247270>.

@article{Bijl1991,
abstract = {We consider separable metrizable topological spaces. Among other things we prove that there exists a non-contractible space with the compact extension property and we prove a new version of realization of polytopes for $\operatorname\{ANR\}$’s.},
author = {Bijl, Jos, van Mill, Jan},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {absolute retract; the compact extension property; contractibility; simplicial complex; partial realization; absolute retract; simplicial complex; compact extension property},
language = {eng},
number = {2},
pages = {369-375},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The compact extension property: the role of compactness},
url = {http://eudml.org/doc/247270},
volume = {32},
year = {1991},
}

TY - JOUR
AU - Bijl, Jos
AU - van Mill, Jan
TI - The compact extension property: the role of compactness
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1991
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 32
IS - 2
SP - 369
EP - 375
AB - We consider separable metrizable topological spaces. Among other things we prove that there exists a non-contractible space with the compact extension property and we prove a new version of realization of polytopes for $\operatorname{ANR}$’s.
LA - eng
KW - absolute retract; the compact extension property; contractibility; simplicial complex; partial realization; absolute retract; simplicial complex; compact extension property
UR - http://eudml.org/doc/247270
ER -

References

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  1. Ancel F.D., The role of countable dimensionality in the theory of cell-like relations, Trans. A.M.S. 287 (1985), 1-40. (1985) Zbl0507.54017MR0766204
  2. van der Bijl J., van Mill J., Linear spaces, absolute retracts and the compact extension property, Proc. A.M.S. 104 (1988), 942-952. (1988) Zbl0689.55001MR0964878
  3. van der Bijl J., Dobrowolski T., Hart K.P., van Mill J., Admissibility, homeomorphism extension and the AR-property in topological linear spaces, submitted to Proc. A.M.S. Zbl0774.55002
  4. van der Bijl J., Extension of continuous functions with compact domain, Ph.D. thesis, Vrije Universiteit, Amsterdam, 1991, to appear. 
  5. Borsuk K., Theory of retracts, PWN, Warszawa, 1967. Zbl0153.52905MR0216473
  6. Curtis D.W., van Mill J., The compact extension property, Proc. Sixth Prague Topology Symposium, Heldermann, Berlin, 1988, pp. 115-119. Zbl0652.55002MR0952598
  7. Dobrowolski T., On extending mappings into nonlocally convex metric spaces, Proc. A.M.S. 93 (1985), 555-560. (1985) MR0774022
  8. Dranishnikov A.N., On a problem of P.S. Alexandrov, Matem. Sbornik 135 (1988), 551-557 (Russian) =Math. USSR Sbornik 63 (1989), 539-545. (1989) MR0942139
  9. Engelking R., General Topology, PWN, Warszawa, 1977. Zbl0684.54001MR0500780
  10. Hu S.-T., Theory of Retracts, Wayne State University Press, Detroit, 1965. Zbl1164.54341MR0181977
  11. Kuratowski K., Sur quelques problèmes topologiques concernant le prolongement des fonctions continus, Colloq. Math. 2 (1951), 186-191. (1951) MR0048791
  12. van Mill J., Another counterexample in ANR-theory, Proc. A.M.S. 97 (1986), 136-138. (1986) Zbl0602.55002MR0831402
  13. van Mill J., Infinite-dimensional topology: prerequisites and introduction, North-Holland Publishing Company, Amsterdam, 1989. Zbl0663.57001MR0977744

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