‎Assume that $A$ is a Banach algebra‎. ‎We define the‎ ‎$beta-$topology and the $gamma-$topology on the space $QM_{el}(A^{*})$ of all bounded extended left quasi-multipliers of $A^{*}.$‎ ‎We establish further properties of $(QM_{el}(A^{*}),gamma)$ when $A$ is a $C^{*}-$algebra‎. ‎In particular‎, ‎we characterize the $gamma-$dual‎ ‎of $QM_{el}(A^{*})$ and prove that $(QM_{el}(A^{*}),gamma)^{*},$...

In this article, the ant colony method is utilized for topology optimization of space structures. Strain energy of the structure is minimized while the material volume is limited to a certain amount. In other words, the stiffest possible structure is sought when certain given materials are used. In addition, a noise cleaning technique is addressed to prevent undesirable members in optimum topol...

In this paper we prove two strict insertion theorems for frame homomorphisms. When applied to the frame of all open subsets of a topological space they are equivalent to the insertion statements of the classical theorems of Dowker and Michael regarding, respectively, normal countably paracompact spaces and perfectly normal spaces. In addition, a study of perfect normality for frames is made.

a. csaszar introduced and extensively studied the notionof generalized open sets. following csazar, we introduce a new notionsuperconnected. the main purpose of this paper is to study generalizedsuperconnected spaces. various characterizations of generalized super-connected spaces and preservation theorems are discussed.

let $l$ be a completely regular frame and $mathcal{r}l$ be the ‎ring of continuous real-valued functions on $l$‎. ‎we show that the‎ ‎lattice $zid(mathcal{r}l)$ of $z$-ideals of $mathcal{r}l$ is a‎ ‎normal coherent yosida frame‎, ‎which extends the corresponding $c(x)$‎ ‎result of mart'{i}nez and zenk‎. ‎this we do by exhibiting‎ ‎$zid(mathcal{r}l)$ as a quotient of $rad(mathcal{r}l)$‎, ‎the‎ ‎...

The purpose of this paper is to construct a weak hyper semi-quantale as a generalization of the concept of semi-quantale and used it as an appropriate hyperlattice-theoretic basis to formulate new lattice-valued topological theories. Based on such weak hyper semi-quantale, we aim to construct the notion of a weak hypervalued-topology as a generalized form of the so-called lattice-valued t...