A homogeneous space of point-countable but not of countable type

Désirée Basile; Jan van Mill

Commentationes Mathematicae Universitatis Carolinae (2007)

  • Volume: 48, Issue: 3, page 459-463
  • ISSN: 0010-2628

Abstract

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We construct an example of a homogeneous space which is of point-countable but not of countable type. This shows that a result of Pasynkov cannot be generalized from topological groups to homogeneous spaces.

How to cite

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Basile, Désirée, and van Mill, Jan. "A homogeneous space of point-countable but not of countable type." Commentationes Mathematicae Universitatis Carolinae 48.3 (2007): 459-463. <http://eudml.org/doc/250194>.

@article{Basile2007,
abstract = {We construct an example of a homogeneous space which is of point-countable but not of countable type. This shows that a result of Pasynkov cannot be generalized from topological groups to homogeneous spaces.},
author = {Basile, Désirée, van Mill, Jan},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {homogeneous; coset space; topological group; homogeneous; coset space; topological group},
language = {eng},
number = {3},
pages = {459-463},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A homogeneous space of point-countable but not of countable type},
url = {http://eudml.org/doc/250194},
volume = {48},
year = {2007},
}

TY - JOUR
AU - Basile, Désirée
AU - van Mill, Jan
TI - A homogeneous space of point-countable but not of countable type
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2007
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 48
IS - 3
SP - 459
EP - 463
AB - We construct an example of a homogeneous space which is of point-countable but not of countable type. This shows that a result of Pasynkov cannot be generalized from topological groups to homogeneous spaces.
LA - eng
KW - homogeneous; coset space; topological group; homogeneous; coset space; topological group
UR - http://eudml.org/doc/250194
ER -

References

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  3. Filippov V.V., The perfect image of a paracompact feathery space Dokl. Akad. Nauk SSSR, 176 (1967), 533-535. (1967) MR0222853
  4. Ford L.R., Jr., Homeomorphism groups and coset spaces, Trans. Amer. Math. Soc. 77 (1954), 490-497. (1954) Zbl0058.17302MR0066636
  5. Henriksen M., Isbell J.R., Some properties of compactifications, Duke Math. J. 25 (1957), 83-105. (1957) MR0096196
  6. Ishii T., On closed mappings and M -spaces. I, II, Proc. Japan Acad. 43 (1967), 752-756; 757-761. (1967) MR0222854
  7. van Mill J., A homogeneous Eberlein compact space which is not metrizable, Pacific J. Math. 101 (1982), 141-146. (1982) Zbl0495.54020MR0671846
  8. van Mill J., Homogeneous subsets of the real line, Compositio Math. 45 (1982), 3-13. (1982) Zbl0528.54034MR0660152
  9. Pasynkov B.A., Almost-metrizable topological groups, Dokl. Akad. Nauk SSSR 161 (1965), 281-284. (1965) Zbl0132.27802MR0204565
  10. Ungar G.S., On all kinds of homogeneous spaces, Trans. Amer. Math. Soc. 212 (1975), 393-400. (1975) Zbl0318.54037MR0385825

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