(a,b)-chain compact

Name

[a,b]-chain compact

Definition

a and b denote infinite cardinals.
A topological space is called [a,b]-chain compact if every chain net with the cardinality from a to b (note that the cardinal may be equal to a or b) has a convergent cofinal subnet.

Reference

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