A surjective characterization of Dugundji spaces
HTML articles powered by AMS MathViewer
- by Burkhard Hoffmann PDF
- Proc. Amer. Math. Soc. 76 (1979), 151-156 Request permission
Abstract:
It is shown that the class of Dugundji spaces coincides with the class of continuous images of the generalized Cantor set by maps satisfying the zero-dimensional lifting property. It follows that each point in a Dugundji space has a neighbourhood base of Dugundji spaces.References
- Seymour Z. Ditor, Averaging operators in $C(S)$ and lower semicontinuous sections of continuous maps, Trans. Amer. Math. Soc. 175 (1973), 195–208. MR 312228, DOI 10.1090/S0002-9947-1973-0312228-8
- Seymour Ditor and Richard Haydon, On absolute retracts, $P(S)$, and complemented subspaces of ${\cal C}(D^{\nu }_{1})$, Studia Math. 56 (1976), no. 3, 243–251. MR 418027, DOI 10.4064/sm-56-3-243-251
- B. A. Efimov, Dyadic bicompacta, Trudy Moskov. Mat. Obšč. 14 (1965), 211–247 (Russian). MR 0202105
- Richard Haydon, On a problem of Pełczyński: Milutin spaces, Dugundji spaces and AE(0-dim), Studia Math. 52 (1974), 23–31. MR 418025, DOI 10.4064/sm-52-1-23-31
- E. Michael, Selected Selection Theorems, Amer. Math. Monthly 63 (1956), no. 4, 233–238. MR 1529282, DOI 10.2307/2310346
- A. Pełczyński, Linear extensions, linear averagings, and their applications to linear topological classification of spaces of continuous functions, Dissertationes Math. (Rozprawy Mat.) 58 (1968), 92. MR 227751
- E. V. Ščepin, Topology of limit spaces with uncountable inverse spectra, Uspehi Mat. Nauk 31 (1976), no. 5 (191), 191–226 (Russian). MR 0464137 G. S. Young, Continuous selections on locally compact separable metric spaces, set-valued mappings, selections and topological properties of ${2^X}$, Lecture Notes in Math., vol. 171, Springer-Verlag, Berlin and New York, 1970, pp. 102-110.
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 76 (1979), 151-156
- MSC: Primary 54C40; Secondary 54C10, 54C55
- DOI: https://doi.org/10.1090/S0002-9939-1979-0534408-X
- MathSciNet review: 534408