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α-realcompact

Last-modified: 2010-12-28 (火) 22:20:15

Definition 1 Edit

A topological space X is α-realcompact (or closed-complete) iff each 2-valued regular Borel measure in X is τ-additive.

Definition 2 Edit

Same as a-realcompact.

Reference Edit

Definition 1
R.J.Gardner and W.F.Pfeffer, Borel Measures, in "Handbook of Set-Theoretic Topology", Elsevier, 1984, 961-1043.
Definition 2
Nancy Dykes, Generalizations of Realcompact Spaces, Pacific Journal of Mathematics Vol. 33, No. 3, 1970.