Pseudocompact space

In mathematics, in the field of topology, a topological space is said to be pseudocompact if its image under any continuous function to R is bounded. Many authors include the request that the space is completely regular right in the definition of pseudocomapctness. Pseudocompact spaces were defined by Edwin Hewitt in 1948.[1]

Properties related to pseudocompactness

Pseudocompact topological groups

A relatively refined theory is available for pseudocompact topological groups.[2] In particular, W. W. Comfort and Kenneth A. Ross proved that a product of pseudocompact topological groups is still pseudocompact (this might fail for arbitrary topological spaces).[3]

Notes

  1. Rings of real-valued continuous functions, I, Trans. Amer. Math. Soc. 64 (1948), 45-99.
  2. See, for example, Mikhail Tkachenko, Topological Groups: Between Compactness and \aleph_0-boundedness, in Mirek Husek and Jan van Mill (eds.), Recent Progress in General Topology II, 2002 Elsevier Science B.V.
  3. Comfort, W. W. and Ross, K. A., Pseudocompactness and uniform contmuity in topological groups, Pacific J. Math. 16, 483-496, 1966.

See also

References

External links

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