Homogeneity and rigidity in Erdös spaces

Klaas Pieter Hart; Jan van Mill

doi:10.14712/1213-7243.2015.265

Homogeneity and rigidity in Erdös spaces

Klaas Pieter Hart, Jan van Mill

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Abstract

The classical Erdös spaces are obtained as the subspaces of real sep- arable Hilbert space consisting of the points with all coordinates rational or all coordinates irrational, respectively. One can create variations by specifying in which set each coordinate is allowed to vary. We investigate the homogeneity of the resulting subspaces. Our two main results are: in case all coordinates are allowed to vary in the same set the subspace need not be homogeneous, and by specifying different sets for different coordinates it is possible to create a rigid subspace.

Original language	English
Pages (from-to)	495-501
Number of pages	7
Journal	Commentationes Mathematicae Universitatis Carolinae
Volume	59
Issue number	4
DOIs	https://doi.org/10.14712/1213-7243.2015.265
Publication status	Published - 2018

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

Erdös space
Homogeneity
Rigidity
Sphere

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10.14712/1213-7243.2015.265

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Homogeneity and rigidity in Erdös spaces

Abstract

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Keywords

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