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 pseudocompactness. Pseudocompact spaces were defined by Edwin Hewitt in 1948.
Contents
Properties related to pseudocompactness
Pseudocompact topological groups
A relatively refined theory is available for pseudocompact topological groups. 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).
References
Pseudocompact space Wikipedia(Text) CC BY-SA