We present instances of the following phenomenon: if a product of topological spaces satisfies some given compactness property then the factors satisfy a stronger compactness property, except possibly for a small number of factors. The first known result of this kind, a consequence of a theorem by A. H. Stone, asserts that if a product is regular and Lindelöf then all but at most countably many...

We study some geometric properties of actions on nonpositively curved spaces related to complete reducibility and semisimplicity, focusing on representations of a finitely generated group Γ in the group G of rational points of a reductive group over a local field, acting on the associated space (symmetric space or affine building). We prove that the space of completely reducible classes is the ...

The lattice of z-ideals of the ring C(X) of real-valued continuous functions on a completely regular Hausdorff space X has been shown by Mart́ınez and Zenk to be a complete Heyting algebra with certain properties. We show that these properties are due only to the fact that C(X) is an f -ring with bounded inversion. This we do by studying lattices of algebraic z-ideals of abstract f -rings with b...

In the literature, different axiomatizations of Public Announcement Logic (PAL) were proposed. Most of these axiomatizations share a ‘core set’ of the so-called reduction axioms. In particular, there is a composition axiom which stipulates how two consecutive announcements are composed into one. In this paper, by designing non-standard Kripke semantics for the language of PAL, we show that with...

Given Banach spaces X, Y and a compact Hausdorff space K, we use polymeasures to give necessary conditions for a multilinear operator from C(K, X) into Y to be completely continuous (resp. unconditionally converging). We deduce necessary and sufficient conditions for X to have the Schur property (resp. to contain no copy of c0), and for K to be scattered. This extends results concerning linear ...

Strongly Unfoldable Cardinals Made Indestructible by Thomas A. Johnstone Advisor: Joel David Hamkins I provide indestructibility results for weakly compact, indescribable and strongly unfoldable cardinals. In order to make these large cardinals indestructible, I assume the existence of a strongly unfoldable cardinal κ, which is a hypothesis consistent with V = L. The main result shows that any ...

This paper contributes to the literature of pro-poor growth measurement by introducing a growth-rate consistency axiom. The axiom states that if one growth pattern is judged to be more pro-poor than another growth pattern at a given growth rate, then the pro-poor ranking between the two growth patterns should remain the same at a higher growth rate. We show that summary pro-poor measures such a...

4 Axioms of ZFC 7 4.1 Axiom of extensionality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4.2 Axiom of the empty set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4.3 Axiom of unordered pairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4.4 Axiom of union . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4.5 Axiom of infinity . . ...