We prove a representation theorem for Boolean contact algebras which implies that the axioms for the Region Connection Calculus [20] (RCC) are complete for the class of subalgebras of the algebras of regular closed sets of weakly regular connected T1 spaces.

The concept of q , -fuzzy ternary subsemigroup (left, right, lateral, quasi-, bi-) ideal of a ternary semigroup is introduced and several related properties are investigated. We give some characterizations of regular and weakly regular ternary semigroups by q , -fuzzy left (right, lateral) ideals, q , -fuzzy quasi-ideals and q , -fuzzy bi-(generalized bi-) ideals.

Let R be an excellent local domain of positive characteristic with residue field k and let R+ be its absolute integral closure. If Tor1 (R +, k) vanishes, then R is weakly F-regular. If R has at most an isolated singularity or has dimension at most two, then R is regular.

The aim of this paper is to introduce and study the new class of sets called gprw-closed sets. This new class of sets lies between the class of regular weakly closed (briefly rw-closed) sets and the class of generalized pre regular closed (briefly gpr-closed) sets. And also we study the fundamental properties of this class of sets. Mathematics Subject Classification: 54A05

Abstract A Grigorchuk–Gupta–Sidki (GGS)-group is a subgroup of the automorphism group p -regular rooted tree for an odd prime , generated by one and directed automorphism. Pervova proved that all torsion GGS-groups do not have maximal subgroups infinite index. Here, we extend result to nontorsion GGS-groups, which include weakly regular branch, but GGS-group.

We consider the question of membership of A ∨ G, where A and G are the pseudovarieties of finite aperiodic semigroups, and finite groups, respectively. We find a straightforward criterion for a semigroup S lying in a class of finite semigroups that are weakly abundant, to be in A ∨ G. The class of weakly abundant semigroups contains the class of regular semigroups, but is much more extensive; w...

Weakly recognizing morphisms from free semigroups onto finite semigroups are a classical way for defining the class of ω-regular languages, i.e., a set of infinite words is weakly recognizable by such a morphism if and only if it is accepted by some Büchi automaton. We consider the descriptional complexity of various constructions for weakly recognizing morphisms. This includes the conversion f...

Let X be a reflexive Banach space which has a weakly sequentially continuous duality mapping. In this paper, we consider the following viscosity approximation sequence x n λ n fx n 1−λ n T n x n , where λ n ∈ 0, 1, {T n } is a uniformly asymptotically regular sequence, and f is a weakly contractive mapping. Strong convergence of the sequence {x n } is proved.

We prove the following: (1) If κ is weakly inaccessible then NSκ is not κ+-saturated. (2) If κ is weakly inaccessible and θ < κ is regular then NSθ κ is not κ +saturated. (3) If κ is singular then NS κ+ is not κ++-saturated. Combining this with previous results of Shelah, one obtains the following: (A) If κ > א1 then NSκ is not κ+-saturated. (B) If θ+ < κ then NSθ κ is not κ +-saturated.

We are proving the following: (1) If κ is a weakly inaccessible then NSκ is not κ -saturated. (2) If κ is a weakly inaccessible and θ < κ is regular then NS κ is not κ saturated. (3) If κ is singular then NS κ+ is not κ-saturated. Combining this with previous results of Shelah, one obtains the following: (A) If κ > א1 then NSκ is not κ -saturated. (B) If θ < κ then NS κ is not κ -saturated.