A surjective characterization of Dugundji spaces

Hoffmann, Burkhard

doi:10.1090/S0002-9939-1979-0534408-X

A surjective characterization of Dugundji spaces
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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

Continuous selections on locally compact separable metric spaces, set-valued mappings, selections and topological properties of