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Last-modified: 2010-12-05 (日) 15:51:57

Definition 1 Edit

A topological space is said to be quasicompact if every open cover has a finite subcover.

Definition 2 Edit

A topological space X is said to be quasicompact if every cover of X by co-zero? sets has a finite subcover.

Remark Edit

Definition 1
  • This property is often called "compactness". But some authors like Bourbaki use "quasicompact", who includes Hausdorffness in the term "compact".
  • This term is often used for non-Hausdorff compact spaces to put stress on non-Hausdorffness. For example, for the spectrum of a ring with Zariski topology.
Definition 2

Reference Edit

Definition 1
  • N. Bourbaki, General Topology(Elements of Mathematics), Springer, 2nd printing (1998).
  • 上野健爾, 代数幾何, 岩波書店(2005).
Definition 2
  • J. K. Hohli and D. Singh, Between compactness and quasicompactness, Acta. Math. Hungar. 106 (4) (2005), 317-329.