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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-2-6,
author = {J. van Mill and G. J. Ridderbos},
title = {Notes on Retracts of Coset Spaces},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {53},
year = {2005},
pages = {169-179},
zbl = {1129.54011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-2-6}
}
J. van Mill; G. J. Ridderbos. Notes on Retracts of Coset Spaces. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 53 (2005) pp. 169-179. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-2-6/