Dense Families of Selections and Finite-Dimensional Spaces

Set-Valued Analysis

Volumn 11, Issue 4, 2003, Pages 373-391

  Gutev, Valentin ^a   Valov, Vesko ^b  

^a UNIVERSITY OF KWAZULU NATAL   (South Africa)

^b NIPISSING UNIVERSITY   (Canada)

Author keywords

Continuous selection; Finite dimensional space; Strongly countable dimensional space; Zn set

Indexed keywords

EID: 1642459132     PISSN: 09276947     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1025679902969     Document Type: Article

References (30)

1. Aló, R. A. and Sennott, L. I.: Extending linear space-valued functions, Math. Ann. 191 (1971), 79-86.
2. n-sets and the disjoint n-cells property in products of ANR's, Mat. Stud. 13(1) (2000), 74-78.
3. Blair, R. L. and Hager, A. W.: Extensions of zero-sets and of real-valued functions, Math. Z. 136 (1974), 41-52.
4. Chigogidze, A.: Inverse Spectra, North-Holland, Amsterdam, 1996.
5. Di Maio, G., Holá, L'., Holý, D. and McCoy, R. A.: Topologies on the space of continuous functions, Topology Appl. 86 (1998), 105-122.
6. Dieudonne, J.: Une généralisation des espaces compacts, J. Math. Pures Appl. 23 (1944), 65-76.
7. Dowker, C. H.: On countably paracompact spaces, Canada. J. Math. 3 (1951), 291-224.
8. Dugundji, J.: Topology, Boston, 1966.
9. Dugundji, J. and Michael, E.: On local and uniformly local topological properties, Proc. Amer. Math. Soc. 7 (1956), 304-307.
10. Engelking, R.: General Topology, revised and completed edn, Heldermann Verlag, Berlin, 1989.
11. Engelking, R.: Theory of Dimensions: Finite and Infinite, Heldermann Verlag, Lemgo, 1995.
12. Gutev, V. and Valov, V.: Continuous selections and C-spaces, Proc. Amer. Math. Soc. 130 (2002), 233-242.
13. Hanai, S.: On closed mappings. II, Proc. Japan Acad. 32 (1956), 388-391.
14. Henderson, D.W.: Z-set's in ANR's, Trans. Amer. Math. Soc. 213 (1975), 205-216.
15. Katětov, M.: On real-valued functions in topological spaces, Fund. Math. 38 (1951), 85-91.
16. Krikorian, N.: A note concerning the fine topology on function spaces, Compositio Math. 21 (1969), 343-348.
17. Michael, E.: Continuous selections I, Ann. of Math. 63 (1956), 361-382.
18. Michael, E.: Continuous selections II, Ann. of Math. 64 (1956), 562-580.
19. Michael, E.: Continuous selections avoiding a set, Topology Appl. 28 (1988), 195-213.
20. Michael, E.: A generalization of a theorem on continuous selections, Proc. Amer. Math. Soc. 105 (1989), 236-243.
21. Morita, K.: On generalizations of Borsuk's homotopy extension theorem, Fund. Math. 88 (1975), 1-6.
22. Munkres, J.: Topology, Prentice Hall, Englewood Cliffs, NY, 1975.
23. Ostrand, P.: Covering dimension in general spaces, Topology Appl. 1 (1971), 209-221.
24. Pol, E.: Characterizing strong countable-dimensionality in terms of Baire category, Fund. Math. 131 (1988), 155-165.
25. Pol, E.: Residuality of the set of embeddings into Nagata's n-dimensional universal spaces, Fund. Math. 129 (1988), 59-67.
26. Przymusiński, T.: Collectionwise normality and extensions of continuous functions, Fund. Math. 98 (1978), 75-81.
27. Repovš, D. and Semenov, P. V.: Continuous Selections of Multivalued Mappings, Mathematics and its Applications 455, Kluwer Academic Publishers, The Netherlands, 1998.
28. Shapiro, H. L.: Extensions of pseudometrics, Canad. J. Math. 18 (1966), 981-998.
29. 2-manifolds, Fund. Math. 101 (1978), 93-110.
30. Uspenskij, V.: A selection theorem for C-spaces, Topology Appl. 85 (1998), 351-374.