Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
absolute retract; the compact extension property; contractibility; simplicial complex; partial realization
absolute retract; the compact extension property; contractibility; simplicial complex; partial realization
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.
References:
[1] Ancel F.D.: The role of countable dimensionality in the theory of cell-like relations. Trans. A.M.S. 287 (1985), 1-40. MR 0766204 | Zbl 0507.54017
[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. MR 0964878 | Zbl 0689.55001
[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
[4] van der Bijl J.: Extension of continuous functions with compact domain. Ph.D. thesis, Vrije Universiteit, Amsterdam, 1991, to appear.
[5] Borsuk K.: Theory of retracts. PWN, Warszawa, 1967. MR 0216473 | Zbl 0153.52905
[6] Curtis D.W., van Mill J.: The compact extension property. Proc. Sixth Prague Topology Symposium, Heldermann, Berlin, 1988, pp. 115-119. MR 0952598 | Zbl 0652.55002
[7] Dobrowolski T.: On extending mappings into nonlocally convex metric spaces. Proc. A.M.S. 93 (1985), 555-560. MR 0774022
[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
[9] Engelking R.: General Topology. PWN, Warszawa, 1977. MR 0500780 | Zbl 0684.54001
[10] Hu S.-T.: Theory of Retracts. Wayne State University Press, Detroit, 1965. MR 0181977 | Zbl 1164.54341
[11] Kuratowski K.: Sur quelques problèmes topologiques concernant le prolongement des fonctions continus. Colloq. Math. 2 (1951), 186-191. MR 0048791
[12] van Mill J.: Another counterexample in ANR-theory. Proc. A.M.S. 97 (1986), 136-138. MR 0831402 | Zbl 0602.55002
[13] van Mill J.: Infinite-dimensional topology: prerequisites and introduction. North-Holland Publishing Company, Amsterdam, 1989. MR 0977744 | Zbl 0663.57001
Search
Partner of
