(a,b)-compact

Name

[a,b]-compact

Definition 1

a and b are cardinals.
A topological space X is called [a,b]-compact (or [a,b]-compact in the sense of open covers) provided that if U is an open cover of X with , then U has a subcover V with .

Definition 2

a and b are infinite cardinals.
A topological space X is called [a,b]-compact if every open cover of X with cardinality at most b has a subcover with cardinality less than a.

Remark

Definition 1

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

Definition 2

• K.P.Hart, J. Nagata and J.E. Vaughan, Encyclopedia of general topology, Elsevier Science