let s be a locally compact topological foundation semigroup with identity and ma(s) be its semigroup algebra. in this paper, we give necessary and sufficient conditions to have abounded approximate identity in closed codimension one ideals of the semigroup algebra $m_a(s)$ of a locally compact topological foundationsemigroup with identity.

We describe the structure of 0-simple countably compact topological inverse semigroups and the structure of congruence-free countably compact topological inverse semigroups. We follow the terminology of [3, 4, 8]. In this paper all topological spaces are Hausdorff. If S is a semigroup then we denote the subset of idempotents of S by E(S). A topological space S that is algebraically a semigroup ...

In this paper we introduce GF-compactifications, which are compactifications of GF-spaces (a new notion introduced by the authors). We study properties of this new kind of compactification and prove that every GF-compactification is of Wallman type. We also prove that every metrizable compactification of a metric space X is a GF-compactification and, as a corollary, that every metric compactifi...

and similarly for the right topological centre Z(r)(A′′). The algebra A is said to be Arens regular if Z(`)(A′′) = Z(r)(A′′) = A′′ and strongly Arens irregular if Z(`)(A′′) = Z(r)(A′′) = A. For example, every C∗-algebra is Arens regular [2]. There has been a great deal of study of these two algebras, especially in the case where A is the group algebra L(G) for a locally compact group G. Results...

Let GL(n, C) ⊃ Un be the group of n× n complex valued invertible matrices and the subgroup of unitary matrices respectively. In this paper we study Finsler p-metrics on the homogeneous space Xn = GL(n, C)/Un for p ∈ [1,∞], which are induced by Schatten p-norms on the tangent bundle of Xn and are invariant under the action of GL(n, C). We show that for p ∈ (1,∞) the Busemann p-compactification i...

I discuss the correspondence between realistic four dimensional free fermionic models and Z2 × Z2 orbifold compactification. I discuss the properties of the Z2 × Z2 orbifold that are reflected in the realistic free fermionic models. I argue that the properties of the realistic free fermionic models arise due to the underlying Z2×Z2 orbifold compactification with nontrivial background fields. I ...