It is well known that a microperiodic function mapping a topological group into reals, which is continuous at some point is constant. We introduce the notion of a microperiodic multifunction, defined on a topological group with values in a metric space, and study regularity conditions implying an analogous result. We deal with Vietoris and Hausdorff continuity concepts.Stability of microperiodi...

Profinite equations are an indispensable tool for the algebraic classification of formal languages. Reiterman’s theorem states that they precisely specify pseudovarieties, i.e. classes of finite algebras closed under finite products, subalgebras and quotients. In this paper Reiterman’s theorem is generalised to finite Eilenberg-Moore algebras for a monad T on a variety D of (ordered) algebras: ...

In the present work, we give necessary and sufficient conditions on the graph of a right-angled Artin group that determine whether the group is subgroup separable or not. Also we show that right-angled Artin groups are residually torsion-free nilpotent. Moreover, we investigate the profinite topology of F2 × F2 and of the group L in [18], which are the only obstructions for the subgroup separab...

Abstract For G a profinite group, we construct an equivalence between rational -Mackey functors and certain full subcategory of -sheaves over the space closed subgroups called Weyl- -sheaves. This consists those sheaves whose stalk subgroup K is -fixed. extends classification for finite Thévenaz Webb, Greenlees May to new class examples. Moreover, this instrumental in -spectra , as given second...

Based on a complete Heyting algebra, we modify the definition oflattice-valued fuzzifying convergence space using fuzzy inclusionorder and construct in this way a Cartesian-closed category, calledthe category of $L-$ordered fuzzifying convergence spaces, in whichthe category of $L-$fuzzifying topological spaces can be embedded.In addition, two new categories are introduced, which are called the...

For an abelian variety A over a number field k we discuss the space of sections of its fundamental group extension π1(A/k). By analyzing the maximal divisible subgroup of the Weil–Châtelet group H(k,A) we show that the space of sections of π1(A/k) contains a copy of Ẑ[k:Q]·dim(A) and is never in bijection with A(k). This is essentially a result about the structure of H(k,T`(A)). 1. Galois secti...