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Abstrakty
We study retracts of coset spaces. We prove that in certain spaces the set of points that are contained in a component of dimension less than or equal to n, is a closed set. Using our techniques we are able to provide new examples of homogeneous spaces that are not coset spaces. We provide an example of a compact homogeneous space which is not a coset space. We further provide an example of a compact metrizable space which is a retract of a homogeneous compact space, but which is not a retract of a homogeneous metrizable compact space.
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Rocznik
Tom
Strony
169--179
Opis fizyczny
Bibliogr. 13 poz.
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autor
- Department of Mathematics, Faculty of Sciences, Vrije Universiteit, De Boelelaan 1081A, 1081 HV Amsterdam, the Netherlands
autor
- Department of Mathematics, Faculty of Sciences, Vrije Universiteit, De Boelelaan 1081A, 1081 HV Amsterdam, the Netherlands
Bibliografia
- [1] A. V. Arkhangel’skiĭ, Cell structures and homogeneity, Mat. Zametki 37 (1985), 580-586, 602 (in Russian).
- [2] —, On power homogeneous spaces, Topology Appl. 122 (2002), 15-33.
- [3] E. G. Effros, Transformation groups and C*-algebras, Ann. of Math. (2) 81 (1965), 38-55.
- [4] R. Engelking, Theory of Dimensions Finite and Infinite, Sigma Series Pure Math. 10, Heldermann, Lemgo, 1995.
- [5] V. Fedorchuk, Bicompacta with noncoinciding dimensionalities, Dokl. Akad. Nauk SSSR 182 (1968), 275-277 (in Russian).
- [6] L. R. Ford, Jr., Homeomorphism groups and coset spaces, Trans. Amer. Math. Soc. 77 (1954), 490-497.
- [7] K. P. Hart and G. J. Ridderbos, A note on an example by van Mill, Topology Appl. 150 (2005), 207-211.
- [8] J. van Mill, On the character and π-weight of homogeneous compacta, Israel J. Math. 133 (2003), 321-338.
- [9] —, A note on Ford’s example, Topology Proc. 28 (2004), 689-694.
- [10] —, A note on the Effros theorem, Amer. Math. Monthly 111 (2004), 801-806.
- [11] G. S. Ungar, On all kinds of homogeneous spaces, Trans. Amer. Math. Soc. 212 (1975), 393-400.
- [12] V. V. Uspenskiĭ, For any X, the product X x Y is homogeneous for some Y, Proc. Amer. Math. Soc. 87 (1983), 187-188.
- [13] S. Watson, The construction of topological spaces: planks and resolutions, in: Recent Progress in General Topology (Prague, 1991), North-Holland, Amsterdam, 1992, 673-757.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-article-BAT5-0006-0050