Approximation of continuous functions on pseudocompact spaces

Pseudocompact Spaces

Purity of the Ideal of Continuous Functions with Pseudocompact Support

Let CΨ (X) be the ideal of functions with pseudocompact support and let kX be the set of all points in υX having compact neighborhoods. We show that CΨ (X) is pure if and only if βX−kX is a round subset of βX, CΨ (X) is a projective C(X)-module if and only if CΨ (X) is pure and kX is paracompact. We also show that if CΨ (X) is pure, then for each f ∈ CΨ (X) the ideal (f ) is a projective (flat)...

Maximal pseudocompact spaces

Maximal pseudocompact spaces (i.e. pseudocompact spaces possessing no strictly stronger pseudocompact topology) are characterized. It is shown that submaximal pseudocompact spaces whose pseudocompact subspaces are closed need not be maximal pseudocompact. Various techniques for constructing maximal pseudocompact spaces are described. Maximal pseudocompactness is compared to maximal feeble compa...

Spaces of Continuous Functions

Let X be a completely regular topological space, B(X) the Banach space of real-valued bounded continuous functions on X, with the usual norm ||&|| =supa?£x|&(#)| • A subset GCB(X) is called completely regular (c.r.) over X if given any closed subset KQ.X and point XoÇzX — K, there exists a ô £ G such that &(#o) = |NI a n ( i sup^^is: \b(x)\ <||&||. A topological space X is completely regular in...

Remarks on Strong Approximation of Continuous Functions

In this note, some embedding relations among many important functional classes are considered. Results of Leindler [7] are extended and improved. 2000 Mathematics Subject Classification: 26A15, 42A10.