*Name [#s3247859]
[a,b]-compact

*Definition 1 [#l9ef1324]
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 &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$a%5cle%20%7cU%7c%5cle%20b$%7d%25.png);, then U has a subcover V with &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$%7cV%7c%5cle%20a$%7d%25.png);.

*Definition 2 [#o1871b36]
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 [#h6d4a33f]
: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