Definition of Pseudocompact. Meaning of Pseudocompact. Synonyms of Pseudocompact

- definition of pseudocompactness. Pseudocompact spaces were defined by Edwin Hewitt in 1948. For a Tychonoff space X to be pseudocompact requires that...
- is not limit point compact. A limit point compact space need not be pseudocompact. An example is given by the same X = Z × Y {\displaystyle X=\mathbb...
- evaluation homomorphism. There are pseudocompact spaces that are not compact, though. In general, for non-pseudocompact spaces there are always maximal ideals...
- compact if every countable open cover has a finite subcover. Pseudocompact. A space is pseudocompact if every continuous real-valued function on the space is...
- uncountable set is hyperconnected, thus connected, locally connected and pseudocompact, but neither weakly countably compact nor countably metacompact, hence...
- be compact it is necessary and sufficient that X be metacompact and pseudocompact (see Watson). A topological space X is said to be of covering dimension...
- {\displaystyle X} such that X × Y {\displaystyle X\times Y} is pseudocompact for every pseudocompact space Y {\displaystyle Y} , and the class C of all spaces...
- paracompact space is compact.[citation needed] Every feebly compact space is pseudocompact but the converse is not necessarily true. For a completely regular Hausdorff...
- we have (A d E or B d E), then we must have A d (X − B) Pseudocompact A space is pseudocompact if every real-valued continuous function on the space is...
- that X is realcompact and pseudocompact (see Engelking, p. 153). Compact space Paracompact space Normal space Pseudocompact space Tychonoff space Gillman...