Homogeneity and rigidity in Erdös spaces

Journal article (2018)

Authors

K.P. Hart Analysis - EEMCS
J. van Mill Universiteit van Amsterdam
Research Group
Analysis (EEMCS) (TU Delft)
Copyright: © 2018 K.P. Hart, J. van Mill
DOI: https://doi.org/10.14712/1213-7243.2015.265
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Published Date

2018

Language

English

Reuse Rights

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

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.

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