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(a,b)-compact

Last-modified: 2011-08-08 (月) 23:35:41

Name Edit

[a,b]-compact

Definition 1 Edit

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 imgtex.fcgi?%5bres=100%5d%7b$a%5cle%20%7cU%7c%5cle%20b$%7d%25.png, then U has a subcover V with imgtex.fcgi?%5bres=100%5d%7b$%7cV%7c%5cle%20a$%7d%25.png.

Definition 2 Edit

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 Edit

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