Spaces of continuous functions

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...

Sübalgebras of Spaces of Continuous Functions

Normed Linear Spaces of Continuous Functions

1. Introduction. In addition to its well known role in analysis, based on measure theory and integration, the study of the Banach space B(X) of real bounded continuous functions on a topological space X seems to be motivated by two major objectives. The first of these is the general question as to relations between the topological properties of X and the properties (algebraic, topological, metr...

P-adic Spaces of Continuous Functions II

Necessary and sufficient conditions are given so that the space C(X, E) of all continuous functions from a zero-dimensional topological space X to a nonArchimedean locally convex space E, equipped with the topology of uniform convergence on the compact subsets of X, to be polarly absolutely quasi-barrelled, polarly אo-barrelled, polarly `∞-barrelled or polarly co-barrelled. Also, tensor product...

Kadec norms on spaces of continuous functions

We study the existence of pointwise Kadec renormings for Banach spaces of the form C(K). We show in particular that such a renorming exists when K is any product of compact linearly ordered spaces, extending the result for a single factor due to Haydon, Jayne, Namioka and Rogers. We show that if C(K1) has a pointwise Kadec renorming and K2 belongs to the class of spaces obtained by closing the ...