| Title:
|
Finite spaces and the universal bundle of a group (English) |
| Author:
|
Witbooi, Peter |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
38 |
| Issue:
|
4 |
| Year:
|
1997 |
| Pages:
|
791-799 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We find sufficient conditions for a cotriad of which the objects are locally trivial fibrations, in order that the push-out be a locally trivial fibration. As an application, the universal $G$-bundle of a finite group $G$, and the classifying space is modeled by locally finite spaces. In particular, if $G$ is finite, then the universal $G$-bundle is the limit of an ascending chain of finite spaces. The bundle projection is a covering projection. (English) |
| Keyword:
|
covering projection |
| Keyword:
|
fibration |
| Keyword:
|
finite space |
| Keyword:
|
push-out |
| MSC:
|
54B15 |
| MSC:
|
54B17 |
| MSC:
|
55R35 |
| MSC:
|
55R40 |
| MSC:
|
55R65 |
| idZBL:
|
Zbl 0938.55024 |
| idMR:
|
MR1603722 |
| . |
| Date available:
|
2009-01-08T18:37:58Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118973 |
| . |
| Reference:
|
[1] Alexandroff P.: Diskrete Räume.Matematiceskii Sbornik (N.S.) 2 (1937), 501-518. Zbl 0018.09105, MR 0004764 |
| Reference:
|
[2] Arhangel'skii A.V., Ponomarev V.I.: Fundamentals of General Topology, Problems and Exercises.D. Reidel Publishing Company, Dordrecht, Holland, 1984. MR 0785749 |
| Reference:
|
[3] Hardie K.A., Vermeulen J.J.C.: Homotopy theory of finite and locally finite T$_0$ spaces.Expo. Math. 11 (1993), 331-341. MR 1240364 |
| Reference:
|
[4] Khalimsky E.D.: Applications of ordered topological spaces in topology.Conference of Math. Departments of Povolsia, 1970. |
| Reference:
|
[5] Massey W.S.: Algebraic Topology, an Introduction.Graduate Texts in Mathematics 70, Springer, 1977. Zbl 0457.55001, MR 0448331 |
| Reference:
|
[6] McCord M.C.: Singular homology groups and homotopy groups of finite topological spaces.Duke Math. J. 33 (1966), 465-474. Zbl 0142.21503, MR 0196744 |
| Reference:
|
[7] Milnor J.W.: Construction of universal bundles I, II.Ann. of Math. 63 (1956), 272-284 and 430-436. MR 0077122 |
| Reference:
|
[8] Stong R.E.: Finite topological spaces.Trans. Amer. Math. Soc. 123 (1966), 325-340. Zbl 0151.29502, MR 0195042 |
| Reference:
|
[9] Steenrod N.E.: The Topology of Fibre Bundles.Princeton University Press, Princeton, New Jersey, 1951. Zbl 0942.55002, MR 0039258 |
| Reference:
|
[10] Witbooi P.J.: Isomorphisms of fibrewise spaces.to appear in Festschrift for G.C.L. Brümmer on his sixtieth birthday, University of Cape Town, Rondebosch, South Africa. Zbl 0988.54012, MR 1722586 |
| . |
