(a,b)^r-compact

Name

-compact

Definition

a and b are infinite cardinal numbers.
A topological space X is called -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 , then E has a complete accumulation point p in X (i.e., for every neighborhood U of p, we have ).

Remark

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