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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Convergence, closed projections and compactness

Author: J. E. Vaughan
Journal: Proc. Amer. Math. Soc. 51 (1975), 469-476
MSC: Primary 54A20; Secondary 54D55
MathSciNet review: 0370462
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Abstract: In this paper several results of N. Noble concerning closed projections are extended using generalizations of first countable, Fréchet, and sequential spaces. We also consider compactness conditions defined by requiring that certain nets have cluster points.

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Keywords: Sequential, Fréchet, first countable spaces, $ \Omega $-net, $ \Omega $-Fréchet, $ \Omega $-neighborhood spaces, closed projections on finite and infinite product spaces, compact, countably compact and initially $ m$-compact spaces, $ \Omega $-compact spaces
Article copyright: © Copyright 1975 American Mathematical Society