Let C(X,Z), C(X,Q) and C(X) denote the l-groups of integer-valued, rationalvalued and real-valued continuous functions on a topological space X, respectively. Characterizations are given for the extensions C(X,Z) 6 C(X,Q) 6 C(X) to be rigid, major, and dense.

Conventional data envelopment analysis (DEA) models normally assume all inputs and outputs are real valued and continuous. However in problems some inputs and outputs can only take integer values, also, both desirable and undesirable outputs can be generated . In this paper the effect of undesirable outputs in integer DEA model is discussed. The proposed model distinguishes weak disposability o...

let s be a semigroup. in certain cases we give some characterizations of extreme amenability of s and we show that in these cases extreme left amenability and extreme right amenability of s are equivalent. also when s is a compact topological semigroup, we characterize extremely left amenable subalgebras of c(s), where c(s) is the space of all continuous bounded real valued functions on s

Let $L$ be a completely regular frame and $mathcal{R}L$ be the ring of continuous real-valued functions on $L$. We study the frame $mathfrak{O}(Min(mathcal{R}L))$ of minimal prime ideals of $mathcal{R}L$ in relation to $beta L$. For $Iinbeta L$, denote by $textit{textbf{O}}^I$ the ideal ${alphainmathcal{R}Lmidcozalphain I}$ of $mathcal{R}L$. We show that sending $I$ to the set of minimal prime ...

in the present paper, among other results, a decomposition formula is given for the w-bounded continuous negative definite functions of a topological *-semigroup s with a weight function w into a proper h*-algebra a in terms of w-bounded continuous positive definite a-valued functions on s. a generalization of a well-known result of k. harzallah is obtained. an earlier conjecture of the author ...