Linear functionals and partitions of unity in Cb(X)

An 𝐿¹-space for Boolean algebras and semireflexivity of spaces 𝐿^{∞}(𝑋,Σ,𝜇)

“…The result above is reminiscent of Katetov's result on the equality Mg = MT, with completeness of (2 playing the role of paracompactness (e.g. see [28]). …”

“…Once things began to come together, the work of D. H. Fremlin [11] provided an inestimable impetus to develop the initial ideas much further. Finally I would like to thank my good friend Bob Wheeler (of [28]) for his generous and steady encouragement in the initiation and completion of this work.…”

“…Introduction. There has been a great deal of work in the past few years on (Cb,M) dual pairings of spaces Cb of bounded continuous functions and spaces M of bounded Baire, or regular Borel, or separable Baire or tight Borel measures defined on completely regular Hausdorff spaces; [3], [12], [26], [27] and [28] contain many references. The topologies of these dual pairings are far from normable, but quite workable versions of these have been found [26] as extensions of Buck's strict topology [2].…”

Vector-valued continuous functions with strict topologies and angelic topological spaces

“…Also the notations and results from [2] will be used. The topologies ß, ß0, ßx, ße (also denoted by ßx) are defined on Cb(X) in [9], [7], [8]-these topologies are defined for K = R, the reals, but naturally extend to K = C, the complex field, ß, ß0, ßx, ßx are defined on Cb(X, E) in [1], [2]. If %°° = %X(X, E) = [H c Cb(X, E): H pointwise equicontinuous and uniformly bounded}, the topology ßx is the finest locally convex topology on Cb(X, E) agreeing with pointwise topology on each H E %°°.…”

A generalized topological measure theory

“…From these beginnings, there has developed in recent years a rather substantial topological measure theory through the efforts of many investigators. Among them should be mentioned Fremlin, Garling and Haydon [4], E. Granirer [6], J. D. Knowles [10], W. Moran [11], [12], F. D. Sentüles [15], [16], [17], R. F. Wheeler [17], [20] and S. Mosiman [13]. Almost all of this work has been done in the context of a completely regular Hausdorff space, and the studies have been concerned with the algebra Cb of bounded, continuous real-valued functions and its dual space.…”