For W a finite set of words, we consider the Rees quotient of a free monoid with respect to the ideal consisting of all words that are not subwords of W . This monoid is denoted by S(W ). It is shown that for every finite set of words W , there are sets of words U ⊃ W and V ⊃ W such that the identities satisfied by S(V ) are finitely based and those of S(U) are not finitely based (regardless of...

In this paper we study the concept of Latin-majorizati-\on. Geometrically this concept is different from other kinds of majorization in some aspects. Since the set of all $x$s Latin-majorized by a fixed $y$ is not convex, but, consists of union of finitely many convex sets. Next, we hint to linear preservers of Latin-majorization on $ mathbb{R}^{n}$ and ${M_{n,m}}$.

is known to have only finitely many triples of positive integer solutions x, y, z for a given n > 2 (Faltings, 1983). In Chapter 11, special situations are described in which more precise information is accessible. For example, if x is in S, then n is bounded by a computable number C5 = Cb(pv ..., p8). From these examples, it should be clear that the book is a mine of information for workers in...

in this paper, the notion of maximal m-open set is introduced and itsproperties are investigated. some results about existence of maximal m-open setsare given. moreover, the relations between maximal m-open sets in an m-spaceand maximal open sets in the corresponding generated topology are considered.our results are supported by examples and counterexamples.

We show that the Cantor-Bendixson rank of a limit group is finite as well as that of a limit group of a linear group. Let T be a universal theory. If T has at most countably many finitely generated models, then one can associate to each finitely generated model M of T an ordinal rank, denoted Rk(M), as defined in [7]. We reformulate the definition of Rk in the context of topological spaces. Let...

For X a compact abelian group and B an infinite subset of its dual X̂, let CB be the set of all x ∈ X such that 〈φ(x) : φ ∈ B〉 converges to 1. If F is a free filter on X̂, let DF = {CB : B ∈ F}. The sets CB and DF are subgroups of X. CB always has Haar measure 0, while the measure of DF depends on F . We show that there is a filter F such that DF has measure 0 but is not contained in any CB . Thi...

For X a compact abelian group and B an infinite subset of its dual X̂, let CB be the set of all x ∈ X such that 〈φ(x) : φ ∈ B〉 converges to 1. If F is a free filter on X̂, let DF = {CB : B ∈ F}. The sets CB and DF are subgroups of X. CB always has Haar measure 0, while the measure of DF depends on F . We show that there is a filter F such that DF has measure 0 but is not contained in any CB . Thi...

Let G = (V,E) be a locally finite graph, i.e. a graph in which every vertex has finitely many adjacent vertices. In this paper, we associate a topology to G, called graphic topology of G and we show that it is an Alexandroff topology, i.e. a topology in which intersec- tion of every family of open sets is open. Then we investigate some properties of this topology. Our motivation is to give an e...