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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Abstract
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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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- Erdös P., 10.2307/1968851, Ann. of Math. (2) 41 (1940), 734–736. MR0003191DOI10.2307/1968851
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- Lawrence L. B., Homogeneity in powers of subspaces of the real line, Trans. Amer. Math. Soc. 350 (1998), no. 8, 3055–3064. MR1458308
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