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2 Bulletin of the Polish Academy of Sciences. Mathematics

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Group structures and rectifiability in powers of spaces

100%

Ridderbos G. J.

Bulletin of the Polish Academy of Sciences. Mathematics

2007

tom Vol. 55, no 4

357-363

We prove that if some power of a space X is rectiflable, then X[sup]πω(x) is rectifiable. It follows that no power of the Sorgenfrey line is a topological group and this answers a question of Arhangeliskiî. We also show that in Mal'tsev spaces of point-countable type, character and π-character coincide.

Notes on retracts of coset spaces

63%

Mill J. v. , Ridderbos G. J.

Bulletin of the Polish Academy of Sciences. Mathematics

2005

tom 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.