Starting with the motivating example of Stone’s representation theorem that allows one to represent Boolean algebras as subalgebras of the poweralgebra of a sufficiently large set, we ask the question of whether it is possible to generalize this to a relationship between lattice theory and topology. This can be done by considering special lattices called locales, which are, in a sense, a suitab...

In  this paper we define the $p$-analog of the restericted reperesentations and also the $p$-analog of the Fourier--Stieltjes algebras on the inverse semigroups . We improve some results about Herz algebras on Clifford semigroups. At the end of this paper we give the necessary and sufficient condition for amenability of these algebras on Clifford semigroups.

Background: Premature birth is a major cause of infant mortality in developed countries. Newborns confined to neonatal intensive care units (NICUs) are in a rapid stage of brain development. As such, sleep plays a pivotal role in the proper brain development of newborns. However, this developmental aspect is often disregarded due to the lack of information. Aim: This study aimed to evaluate the...

Motivated by an Arens regularity problem, we introduce the concepts of matrix Banach space and matrix Banach algebra. The notion of matrix normed space in the sense of Ruan is a special case of our matrix normed system. A matrix Banach algebra is a matrix Banach space with a completely contractive multiplication. We study the structure of matrix Banach spaces and matrix Banach algebras. Then we...

‎in this paper‎, ‎using fixed point method‎, ‎we prove the generalized hyers-ulam stability of‎ ‎random homomorphisms in random $c^*$-algebras and random lie $c^*$-algebras‎ ‎and of derivations on non-archimedean random c$^*$-algebras and non-archimedean random lie c$^*$-algebras for‎ ‎the following $m$-variable additive functional equation:‎ ‎$$sum_{i=1}^m f(x_i)=frac{1}{2m}left[sum_{i=1}^mfle...

Laboratory mice are well capable of performing innate routine behaviour programmes necessary for courtship, nest-building and exploratory activities although housed for decades in animal facilities. We found that in mice inactivation of the clock gene Period1 profoundly changes innate routine behaviour programmes like those necessary for courtship, nest building, exploration and learning. These...

The Stone Representation Theorem for Boolean Algebras, first proved by M. H. Stone in 1936 ([4]), states that every Boolean algebra is isomorphic to a field of sets. This paper motivates and presents a proof.