A surjective characterization of Dugundji spaces

Author:
Burkhard Hoffmann

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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

**[1]**S. Z. Ditor,*Averaging operators in**and lower semicontinuous sections of continuous maps*, Trans. Amer. Math. Soc.**175**(1973), 195-208. MR**0312228 (47:790)****[2]**S. Ditor and R. Haydon,*On absolute retracts*, ,*and complemented subspaces of*, Studia Math.**56**(1976), 243-251. MR**0418027 (54:6071)****[3]**B. A. Efimov,*Dyadic bicompacta*, Trans. Moscow Math. Soc.**14**(1965), 229-267. MR**0202105 (34:1979)****[4]**R. Haydon,*On a problem of Pełczyński*:*Milutin spaces, Dugundji spaces and*, Studia Math.**52**(1974), 23-31. MR**0418025 (54:6069)****[5]**E. Michael,*Selected selection theorems*, Amer. Math. Monthly**63**(1956), 233-238. MR**1529282****[6]**A. Pełczyński,*Linear extensions, linear averagings, and their applications to linear topological classification of spaces of continuous functions*, Dissertationes Math. (Rozprawy Mat.)**58**(1968). MR**0227751 (37:3335)****[7]**E. V. Shchepin,*Topology of limit spaces of uncountable inverse spectra*, Russian Math. Surveys**315**(1976), 155-191. MR**0464137 (57:4072)****[8]**G. S. Young,*Continuous selections on locally compact separable metric spaces, set-valued mappings, selections and topological properties of*, Lecture Notes in Math., vol. 171, Springer-Verlag, Berlin and New York, 1970, pp. 102-110.

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
54C40,
54C10,
54C55

Retrieve articles in all journals with MSC: 54C40, 54C10, 54C55

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1979-0534408-X

Keywords:
Zero-dimensional lifting property,
regular averaging operator,
Dugundji space

Article copyright:
© Copyright 1979
American Mathematical Society