In generalized semi-infinite programming the feasible set is known to be not closed in general. In this paper, under natural and generic assumptions, the closure of the feasible set is described in explicit terms.

in this paper, we introduce and study the concept of $r$-fuzzy regular semi open (closed) sets in smooth topological spaces. by using $r$-fuzzy regular semi open (closed) sets, we define a new fuzzy closure operator namely $r$-fuzzy regular semi interior (closure) operator. also, we introduce fuzzy regular semi continuous and fuzzy regular semi irresolute mappings. moreover, we investigate the ...

Below let II = [0, 1]. A well-known topological theorem due to Katětov states: Suppose (X, τ) is a normal topological space, and let f : X → II be upper semicontinuous, g : X → II be lower semicontinuous, and f ≤ g. Then there is a continuous h : X → II such that f ≤ h ≤ g. Recall that f : X → II is upper semicontinuous if f is continuous from (X, τ) to (II, ω); lower semicontinuous if continuo...

Kummer, M. and F. Stephan, Weakly semirecursive sets and r.e. orderings, Annals of Pure and Applied Logic 60 (1993) 133-150. Weakly semirecursive sets have been introduced by Jockusch and Owings (1990). In the present paper their investigation is pushed forward by utilizing r.e. partial orderings, which turn out to be instrumental for the study of degrees of subclasses of weakly semirecursive s...

In this paper we prove the existence and upper semicontinuity of compact global attractors for the flow of the equation ∂u(x, t) ∂t = −u(x, t) + J ∗ (f ◦ u)(x, t) + h, h ≥ 0, in L weighted spaces.

By an infinitely distributive inverse semigroup will be meant an inverse semigroup S such that for every subset X ⊆ S and every s ∈ S, if ∨ X exists then so does ∨ (sX), and furthermore ∨ (sX) = s ∨ X. One important aspect is that the infinite distributivity of E(S) implies that of S; that is, if the multiplication of E(S) distributes over all the joins that exist in E(S) then S is infinitely d...