# Homogeneity and rigidity in Erdös spaces

Commentationes Mathematicae Universitatis Carolinae (2018)

- Volume: 59, Issue: 4, page 495-501
- ISSN: 0010-2628

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topHart, Klaas P., and van Mill, Jan. "Homogeneity and rigidity in Erdös spaces." Commentationes Mathematicae Universitatis Carolinae 59.4 (2018): 495-501. <http://eudml.org/doc/294808>.

@article{Hart2018,

abstract = {The classical Erdös spaces are obtained as the subspaces of real separable 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.},

author = {Hart, Klaas P., van Mill, Jan},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {Erdös space; homogeneity; rigidity; sphere},

language = {eng},

number = {4},

pages = {495-501},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Homogeneity and rigidity in Erdös spaces},

url = {http://eudml.org/doc/294808},

volume = {59},

year = {2018},

}

TY - JOUR

AU - Hart, Klaas P.

AU - van Mill, Jan

TI - Homogeneity and rigidity in Erdös spaces

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2018

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 59

IS - 4

SP - 495

EP - 501

AB - The classical Erdös spaces are obtained as the subspaces of real separable 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.

LA - eng

KW - Erdös space; homogeneity; rigidity; sphere

UR - http://eudml.org/doc/294808

ER -

## References

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- Engelking R., General Topology, Sigma Series in Pure Mathematics, 6, Heldermann Verlag, Berlin, 1989. Zbl0684.54001MR1039321
- Erdös P., 10.2307/1968851, Ann. of Math. (2) 41 (1940), 734–736. MR0003191DOI10.2307/1968851
- Lavrentieff, M. A., 10.4064/fm-6-1-149-160, Fund. Math. 6 (1924), 149–160 (French). DOI10.4064/fm-6-1-149-160
- Lawrence L. B., Homogeneity in powers of subspaces of the real line, Trans. Amer. Math. Soc. 350 (1998), no. 8, 3055–3064. MR1458308
- Sierpiński W., 10.4064/fm-19-1-65-71, Fund. Math. 19 (1932), 65–71 (French). DOI10.4064/fm-19-1-65-71

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