Topology Proceedings
Document # baak-11
Electronic Version 24 Summer (1999) |
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Realcompactness and Monolithity are finitely additive in Cp(X)
Fidel Casarrubias-Segura
In this paper we prove the finite additivity for realcompactness as well as for paracompactness, Dieudonné-completeness and monolithity in the class of the spaces Cp(X). It was proved in [Tkachuk, 1983] that X is discrete in case that Cp(X) is homeomorphic to R\tau for some cardinal \tau. We generalize this result showing that X is discrete also when Cp(X) is a finite union of subspaces homeomorphic to R\taui for some cardinals \taui. We also establish that if Cp(X) is a countable union of Eberlein-Grothendieck subspaces then Cp(X) is itself an Eberlein-Grothendieck space.
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Date published electronically: March 5, 2001.