Universal uniform Eberlein compact spaces

Bell, M.

doi:10.1090/S0002-9939-00-05403-4

Universal uniform Eberlein compact spaces
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by M. Bell PDF

Proc. Amer. Math. Soc. 128 (2000), 2191-2197 Request permission

Abstract:

A universal space is one that continuously maps onto all others of its own kind and weight. We investigate when a universal Uniform Eberlein compact space exists for weight $\kappa$. If $\kappa = 2^{<\kappa }$, then they exist whereas otherwise, in many cases including $\kappa = \omega _1$, it is consistent that they do not exist. This answers (for many $\kappa$ and consistently for all $\kappa$) a question of Benyamini, Rudin and Wage of 1977.

References

Spiros A. Argyros and Yoav Benyamini, Universal WCG Banach spaces and universal Eberlein compacts, Israel J. Math. 58 (1987), no. 3, 305–320. MR 917361, DOI 10.1007/BF02771694
Y. Benyamini, M. E. Rudin, and M. Wage, Continuous images of weakly compact subsets of Banach spaces, Pacific J. Math. 70 (1977), no. 2, 309–324. MR 625889
M.Dzamonja, On uniform Eberlein compacta and c-algebras, to appear in Topology Proceedings.
Menachem Kojman and Saharon Shelah, Nonexistence of universal orders in many cardinals, J. Symbolic Logic 57 (1992), no. 3, 875–891. MR 1187454, DOI 10.2307/2275437
S. Negrepontis, Banach spaces and topology, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 1045–1142. MR 776642
Saharon Shelah, On universal graphs without instances of CH, Ann. Pure Appl. Logic 26 (1984), no. 1, 75–87. MR 739914, DOI 10.1016/0168-0072(84)90042-3
Saharon Shelah, Universal graphs without instances of $\textrm {CH}$: revisited, Israel J. Math. 70 (1990), no. 1, 69–81. MR 1057268, DOI 10.1007/BF02807219