| Title:
|
The compact extension property: the role of compactness (English) |
| Author:
|
van der Bijl, Jos |
| Author:
|
van Mill, Jan |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
2 |
| Year:
|
1991 |
| Pages:
|
369-375 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider separable metrizable topological spaces. Among other things we prove that there exists a non-contractible space with the compact extension property and we prove a new version of realization of polytopes for $\operatorname{ANR}$'s. (English) |
| Keyword:
|
absolute retract |
| Keyword:
|
the compact extension property |
| Keyword:
|
contractibility |
| Keyword:
|
simplicial complex |
| Keyword:
|
partial realization |
| MSC:
|
54C55 |
| MSC:
|
55M15 |
| MSC:
|
57N17 |
| MSC:
|
57N20 |
| idZBL:
|
Zbl 0753.55002 |
| idMR:
|
MR1137798 |
| . |
| Date available:
|
2009-01-08T17:45:02Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/116978 |
| . |
| Reference:
|
[1] Ancel F.D.: The role of countable dimensionality in the theory of cell-like relations.Trans. A.M.S. 287 (1985), 1-40. Zbl 0507.54017, MR 0766204 |
| Reference:
|
[2] van der Bijl J., van Mill J.: Linear spaces, absolute retracts and the compact extension property.Proc. A.M.S. 104 (1988), 942-952. Zbl 0689.55001, MR 0964878 |
| Reference:
|
[3] van der Bijl J., Dobrowolski T., Hart K.P., van Mill J.: Admissibility, homeomorphism extension and the AR-property in topological linear spaces.submitted to Proc. A.M.S. Zbl 0774.55002 |
| Reference:
|
[4] van der Bijl J.: Extension of continuous functions with compact domain.Ph.D. thesis, Vrije Universiteit, Amsterdam, 1991, to appear. |
| Reference:
|
[5] Borsuk K.: Theory of retracts.PWN, Warszawa, 1967. Zbl 0153.52905, MR 0216473 |
| Reference:
|
[6] Curtis D.W., van Mill J.: The compact extension property.Proc. Sixth Prague Topology Symposium, Heldermann, Berlin, 1988, pp. 115-119. Zbl 0652.55002, MR 0952598 |
| Reference:
|
[7] Dobrowolski T.: On extending mappings into nonlocally convex metric spaces.Proc. A.M.S. 93 (1985), 555-560. MR 0774022 |
| Reference:
|
[8] Dranishnikov A.N.: On a problem of P.S. Alexandrov.Matem. Sbornik 135 (1988), 551-557 (Russian) =Math. USSR Sbornik 63 (1989), 539-545. MR 0942139 |
| Reference:
|
[9] Engelking R.: General Topology.PWN, Warszawa, 1977. Zbl 0684.54001, MR 0500780 |
| Reference:
|
[10] Hu S.-T.: Theory of Retracts.Wayne State University Press, Detroit, 1965. Zbl 1164.54341, MR 0181977 |
| Reference:
|
[11] Kuratowski K.: Sur quelques problèmes topologiques concernant le prolongement des fonctions continus.Colloq. Math. 2 (1951), 186-191. MR 0048791 |
| Reference:
|
[12] van Mill J.: Another counterexample in ANR-theory.Proc. A.M.S. 97 (1986), 136-138. Zbl 0602.55002, MR 0831402 |
| Reference:
|
[13] van Mill J.: Infinite-dimensional topology: prerequisites and introduction.North-Holland Publishing Company, Amsterdam, 1989. Zbl 0663.57001, MR 0977744 |
| . |
