Vol. 60, No. 1, 1975

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Compactness-like properties for generalized weak topological sums

W. Wistar (William) Comfort

Vol. 60 (1975), No. 1, 31–37
Abstract

It is shown that under suitable conditions (involving cardinal numbers) on a family of spaces {Xi : i I} with pi Xi for i I, their γ-weak sum {x ΠiIXi : |{i I : xipi}| < γ} is α-compact in the κ-box topology. For example, there is Corollary 2.5: If α is regular and uncountable and |Xi| < α for all i I, then the ω-weak sum (= direct sum) is α-compact in the α-box topology; in particular, the direct sum of any set of finite spaces is α-compact in the α-complete topology for regular α > ω.

Mathematical Subject Classification 2000
Primary: 54B10
Milestones
Received: 3 June 1974
Published: 1 September 1975
Authors
W. Wistar (William) Comfort