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Nonhomogeneity of Remainders, II

Arhangel'skii A. V., Mill J. van

Bulletin of the Polish Academy of Sciences. Mathematics

2015

Vol. 63, no. 1

67--71

We present an example of a separable metrizable topological group G having the property that no remainder of it is (topologically) homogeneous.

Polish Topology

Mill J. van.

Wiadomości Matematyczne

2012

T. 48, Nr 2

199--207

On countable dense and strong local homogeneity

Mill J. van

Bulletin of the Polish Academy of Sciences. Mathematics

2005

Vol. 53, no 4

401-408

We present an example of a connected, Polish, countable dense homogeneous space X that is not strongly locally homogeneous. In fact, a nontrivial homeomorphism of X is the identity on no nonempty open subset of X.

Notes on retracts of coset spaces

Mill J. van, Ridderbos G. J.

Bulletin of the Polish Academy of Sciences. Mathematics

2005

Vol. 53, no 2

169-179

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.