Geodesic
Notes on Retracts of Coset Spaces
J. van Mill1 ; G. J. Ridderbos2
1 Department of Mathematics Faculty of Sciences Vrije Universiteit De Boelelaan 1081A 1081 HV Amsterdam, the Netherlands
2 Department of Mathematics Vrije Universiteit De Boelelaan 1081A 1081 HV Amsterdam the Netherlands
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 53 (2005) no. 2, pp. 169-179

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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.
DOI : 10.4064/ba53-2-6
Keywords: study retracts coset spaces prove certain spaces set points contained component dimension equal closed set using techniques able provide examples homogeneous spaces coset spaces provide example compact homogeneous space which coset space further provide example compact metrizable space which retract homogeneous compact space which retract homogeneous metrizable compact space

J. van Mill 1 ; G. J. Ridderbos 2

1 Department of Mathematics Faculty of Sciences Vrije Universiteit De Boelelaan 1081A 1081 HV Amsterdam, the Netherlands
2 Department of Mathematics Vrije Universiteit De Boelelaan 1081A 1081 HV Amsterdam the Netherlands 
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J. van Mill; G. J. Ridderbos. Notes on Retracts of Coset Spaces. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 53 (2005) no. 2, pp. 169-179. doi: 10.4064/ba53-2-6

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