On strongly ech-complete spaces

A Tychonoff space X is called strongly ech-complete if there exist paracompact open subsets V1, V2, ... of beta X such that boolean AND(infinity)(n=1) V-n = X. Strong (tech-completeness of a Tychonoff space is characterized in terms of the existence of certain kinds of complete sequence of open covers, for example, of a complete sequence consisting of star-finite open covers. A metrizable space is shown to be strongly (tech-complete if, and only if, the space is (tech-complete and strongly metrizable. Universal spaces for strongly (tech-complete metrizable spaces are indicated. A compatible complete metric is constructed for R such that, for each r > 0, every open r-ball meets at most 25 distinct r-balls. This metric is used to derive characterizations for strongly (tech-complete metrizable spaces and strongly metrizable spaces in terms of special compatible metrics. (C) 2020 Elsevier B.V. All rights reserved.Peer reviewe

Mackey-complete spaces and power series -- A topological model of Differential Linear Logic

In this paper, we have described a denotational model of Intuitionist Linear Logic which is also a differential category. Formulas are interpreted as Mackey-complete topological vector space and linear proofs are interpreted by bounded linear functions. So as to interpret non-linear proofs of Linear Logic, we have used a notion of power series between Mackey-complete spaces, generalizing the notion of entire functions in C. Finally, we have obtained a quantitative model of Intuitionist Differential Linear Logic, where the syntactic differentiation correspond to the usual one and where the interpretations of proofs satisfy a Taylor expansion decomposition

Sections, Selections and Prohorov's Theorem

The famous Prohorov theorem for Radon probability measures is generalized in terms of usco mappings. In the case of completely metrizable spaces this is achieved by applying a classical Michael result on the existence of usco selections for l.s.c. mappings. A similar approach works when sieve-complete spaces are considered

Cohomological uniqueness, Massey products and the modular isomorphism problem for 2-groups of maximal nilpotency class

Let $G$ be a finite 2-group of maximal nilpotency class, and let $BG$ be its classifying space. We prove that iterated Massey products in H^*(BG;\F_2) do characterize the homotopy type of $BG$ among 2-complete spaces with the same cohomological structure. As a consequence we get an alternative proof of the modular isomorphism problem for 2-groups of maximal nilpotency class