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Aleph_1-compact

Last-modified: 2010-09-05 (日) 01:06:01

Name Edit

imgtex.fcgi?%5bres=100%5d%7b$%5caleph%20_1$%7d%25.png-compact

Definition Edit

Every uncountable set has a limit point.

Definition 2? Edit

A space X is imgtex.fcgi?%5bres=100%5d%7b$%5caleph%20_1$%7d%25.png-compact if every closed discrete subset of X is countable.

Reference Edit

Definition
R. W. Heath, Separability and \aleph_1 compactness, Colloq. Math. 12 (1964) 11-14. [#ua6ab39c]
Lynn Arthur Steen and J. Arthur Seebach, Jr. Counterexamples in Topology, Dover.
Definition 2
Gale, Sherry L. , Measure-compact spaces. ,[J] Topology Appl. 45, No.2, 103-118 (1992).