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(a,b)^r-compact

Last-modified: 2015-11-17 (火) 18:09:01

Name Edit

imgtex.fcgi?%5bres=100%5d%7b$%5ba%2cb%5d%5er$%7d%25.png-compact

Definition Edit

a and b are infinite cardinal numbers.
A topological space X is called imgtex.fcgi?%5bres=100%5d%7b$%5ba%2cb%5d%5er$%7d%25.png-compact (or [a,b]-compact in the sense of complete accumulation points) provided that if E is an infinite subset of X and if |E| is a regular cardinal with imgtex.fcgi?%5bres=100%5d%7b$a%5cle%20%7cE%7c%5cle%20b$%7d%25.png, then E has a complete accumulation point p in X (i.e., for every neighborhood U of p, we have imgtex.fcgi?%5bres=100%5d%7b$%7cU%5ccup%20E%7c=%7cE%7c$%7d%25.png).

Remark Edit

J. E. Vaughan, Products of [a, b]-Chain Compact Spaces, Soc. Czechoslovak Mathematicians and Physicist, Praha, 1977. pp.473-476.