| Title:
|
Strong shape of the Stone-Čech compactification (English) |
| Author:
|
Mardešić, Sibe |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
33 |
| Issue:
|
3 |
| Year:
|
1992 |
| Pages:
|
533-539 |
| . |
| Category:
|
math |
| . |
| Summary:
|
J. Keesling has shown that for connected spaces $X$ the natural inclusion $e:X\rightarrow \beta X$ of $X$ in its Stone-Čech compactification is a shape equivalence if and only if $X$ is pseudocompact. This paper establishes the analogous result for strong shape. Moreover, pseudocompact spaces are characterized as spaces which admit compact resolutions, which improves a result of I. Lončar. (English) |
| Keyword:
|
inverse system |
| Keyword:
|
resolution |
| Keyword:
|
Stone-Čech compactification |
| Keyword:
|
pseudocompact space |
| Keyword:
|
shape |
| Keyword:
|
strong shape |
| MSC:
|
54B35 |
| MSC:
|
54C56 |
| MSC:
|
54D30 |
| MSC:
|
54D35 |
| MSC:
|
55P55 |
| idZBL:
|
Zbl 0783.54017 |
| idMR:
|
MR1209294 |
| . |
| Date available:
|
2009-01-08T17:57:50Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118520 |
| . |
| Reference:
|
[1] Dowker C.H.: Mapping theorems for noncompact spaces.Amer. J. Math. 69 (1947), 200-240. MR 0020771 |
| Reference:
|
[2] Engelking R.: General Topology.Polish Sci. Publ., Warsaw, 1977. Zbl 0684.54001, MR 0500780 |
| Reference:
|
[3] Glicksberg I.: Stone-Čech compactifications of products.Trans. Amer. Math. Soc. 90 (1959), 369-382. Zbl 0089.38702, MR 0105667 |
| Reference:
|
[4] Keesling J.: Shape theory and the Stone-Čech compactification.in Proc. Internat. Conference on Geometric Topology, Polish Sci. Publ., Warsaw, 1980, pp. 236-243. Zbl 0477.54018, MR 0656750 |
| Reference:
|
[5] Keesling K., Sher R.B.: Shape properties of the Stone-Čech compactification.General Topology and Appl. 9 (1978), 1-8. Zbl 0396.54018, MR 0478105 |
| Reference:
|
[6] Lisica Ju.T., Mardešić S.: Coherent prohomotopy and a strong shape category of topological spaces.in Proc. Internat. Topological Conference (Leningrad 1982), Lecture Notes in Math. 1060, Springer-Verlag, Berlin, 1984, pp. 164-173. MR 0770236 |
| Reference:
|
[7] Lisica Ju.T., Mardešić S.: Coherent prohomotopy and strong shape theory.Glasnik Mat. 19 (39) (1984), 335-399. MR 0790021 |
| Reference:
|
[8] Lončar I.: Some results on resolution of spaces.Rad Jugoslav. Akad. Znan. Umjetn. Matem. Znan. 428 (6) (1987), 37-49. MR 0960457 |
| Reference:
|
[9] Mardešić S.: Approximate polyhedra, resolutions of maps and shape fibrations.Fund. Math. 114 (1981), 53-78. MR 0643305 |
| Reference:
|
[10] Mardešić S., Segal J.: Shape Theory.North-Holland, Amsterdam, 1982. MR 0676973 |
| Reference:
|
[11] Morita K.: On shapes of topological spaces.Fund. Math. 86 (1975), 251-259. Zbl 0296.54034, MR 0388385 |
| Reference:
|
[12] Walker R.C.: The Stone-Čech compactification.Springer-Verlag, Berlin, 1974. Zbl 0292.54001, MR 0380698 |
| . |
