About DML-CZ | FAQ | Conditions of Use | Math Archives | Contact Us
  Previous |  Up |  Next

Article

Basile, Désirée ; van Mill, Jan
A homogeneous space of point-countable but not of countable type. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 48 (2007), issue 3, pp. 459-463
MSC: 54D40, 54D99 | MR 2374127 | Zbl 1199.54159
Keywords:
homogeneous; coset space; topological group
Summary:
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.
References:
[1] Effros E.G.: Transformation groups and $C^*$-algebras. Annals of Math. 81 (1965), 38-55. MR 0174987 | Zbl 0152.33203
[2] van Engelen F., van Mill J.: Borel sets in compact spaces: some Hurewicz-type theorems. Fund. Math. 124 (1984), 271-286. MR 0774518 | Zbl 0559.54034
[3] Filippov V.V.: The perfect image of a paracompact feathery space Dokl. Akad. Nauk SSSR. 176 (1967), 533-535. MR 0222853
[4] Ford L.R., Jr.: Homeomorphism groups and coset spaces. Trans. Amer. Math. Soc. 77 (1954), 490-497. MR 0066636 | Zbl 0058.17302
[5] Henriksen M., Isbell J.R.: Some properties of compactifications. Duke Math. J. 25 (1957), 83-105. MR 0096196
[6] Ishii T.: On closed mappings and $M$-spaces. I, II. Proc. Japan Acad. 43 (1967), 752-756; 757-761. MR 0222854
[7] van Mill J.: A homogeneous Eberlein compact space which is not metrizable. Pacific J. Math. 101 (1982), 141-146. MR 0671846 | Zbl 0495.54020
[8] van Mill J.: Homogeneous subsets of the real line. Compositio Math. 45 (1982), 3-13. MR 0660152 | Zbl 0528.54034
[9] Pasynkov B.A.: Almost-metrizable topological groups. Dokl. Akad. Nauk SSSR 161 (1965), 281-284. MR 0204565 | Zbl 0132.27802
[10] Ungar G.S.: On all kinds of homogeneous spaces. Trans. Amer. Math. Soc. 212 (1975), 393-400. MR 0385825 | Zbl 0318.54037
Partner of
EuDML logo