We show that if a variety V of monotone lattice expansions is finitely generated, then profinite completions agree with canonical extensions on V . The converse holds for varieties of finite type. It is a matter of folklore that the profinite completion of a Boolean algebra B is given by the power set of the Stone space of B, or in the terminology of Jónsson and Tarski [5], by the canonical ext...

The aim of this thesis is to study profinite groups of type FPn. These are groups G which admit a projective resolution P of Ẑ as a ẐJGK-module such that P0, . . . , Pn are finitely generated, so this property can be studied using the tools of profinite group cohomology. In studying profinite groups it is often useful to consider their cohomology groups with profinite coefficients, but pre-exis...

in this paper, the gradual real numbers are considered and the notion of the gradual normed linear space is given. also some topological properties of such spaces are studied, and it is shown that the gradual normed linear space is a locally convex space, in classical sense. so the results in locally convex spaces can be translated in gradual normed linear spaces. finally, we give an examp...

In this paper, we formalize the Menger probabilistic normed space as a category in which its objects are the Menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. Then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. So, we can easily apply the results of topological vector spaces...

Less than continuum many translates of a compact nullset may cover any infinite profinite group Abstract We show that it is consistent with the axioms of set theory that every infinite profinite group G possesses a closed subset X of Haar measure zero such that less than continuum many translates of X cover G. This answers a question of Elekes and Tóth and by their work settles the problem for ...

We solve an open problem of Herfort and Ribes: Profinite Frobenius groups of certain type do occur as closed subgroups of free profinite products of two profinite groups. This also solves a question of Pop about prosolvable subgroups of free profinite products.

on a hypergroupoid one can define a topology such that the hyperoperationis pseudocontinuous or continuous. in this paper we extend thisconcepts to the fuzzy case. we give a connection between the classical and thefuzzy (pseudo)continuous hyperoperations.

the notion of a probabilistic metric  space  corresponds to thesituations when we do not know exactly the  distance.  probabilistic metric space was  introduced by karl menger. alsina, schweizer and sklar gave a general definition of  probabilistic normed space based on the definition of menger [1]. in this note we study the pn spaces which are  topological vector spaces and the open mapping an...

In this paper we introduce a new definition of the first non-abelian cohomology of topological groups.  We relate the cohomology of a normal subgroup $N$ of a topological group $G$ and the quotient $G/N$ to the cohomology of $G$. We get the inflation-restriction exact sequence. Also, we obtain a seven-term exact cohomology sequence up to dimension 2. We give an interpretation of the first non-a...

Let R be a real closed field and L be a finite extension of R(t). We prove that Gal(L) ∼= Gal(R(t)) if L is formally real and Gal(L) is the free profinite group of rank card(R) if L is not formally real. MR Classification: 12E30 Directory: \Jarden\Diary\RealFree 3 April, 2007 * Research supported by the Minkowski Center for Geometry at Tel Aviv University, established by the Minerva Foundation....