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Compactifications and uniformities on sigma frames

Joanne L. Walters-Wayland (1991)

Commentationes Mathematicae Universitatis Carolinae

A bijective correspondence between strong inclusions and compactifications in the setting of σ -frames is presented. The category of uniform σ -frames is defined and a description of the Samuel compactification is given. It is shown that the Samuel compactification of a uniform frame is completely determined by the σ -frame consisting of its uniform cozero part, and consequently, any compactification of any frame is so determined.

Compactifications of ℕ and Polishable subgroups of S

Todor Tsankov (2006)

Fundamenta Mathematicae

We study homeomorphism groups of metrizable compactifications of ℕ. All of those groups can be represented as almost zero-dimensional Polishable subgroups of the group S . As a corollary, we show that all Polish groups are continuous homomorphic images of almost zero-dimensional Polishable subgroups of S . We prove a sufficient condition for these groups to be one-dimensional and also study their descriptive complexity. In the last section we associate with every Polishable ideal on ℕ a certain Polishable...

Compactness and convergence of set-valued measures

Kenny Koffi Siggini (2009)

Colloquium Mathematicae

We prove criteria for relative compactness in the space of set-valued measures whose values are compact convex sets in a Banach space, and we generalize to set-valued measures the famous theorem of Dieudonné on convergence of real non-negative regular measures.

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