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...

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.

We prove that every multi-player perfect-information game with bounded and lower-semi-continuous payoffs admits a subgame-perfect ε-equilibrium in pure strategies. This result complements Example 3 in Solan and Vieille (2003), which shows that a subgame-perfect ε-equilibrium in pure strategies need not exist when the payoffs are not lower-semi-continuous. In addition, if the range of payoffs is...

We give a new proof of sequential weak* lower semicontinuity in BV(Ω;Rm) for integral functionals of the form F(u) := ∫

In this paper, we introduce the notion of fuzzy (r, s)-S1-pre-semicontinuous mappings on intuitionistic fuzzy topological spaces in Šostak’s sense, which is a generalization of S1-pre-semicontinuous mappings by Shi-Zhong Bai. The relationship between fuzzy (r, s)-pre-semicontinuous mapping and fuzzy (r, s)-S1-pre-semicontinuous mapping is discussed. The characterizations for the fuzzy (r, s)-S1...

We introduce the notion of mIT -structures determined by operators mInt and mCl on an m-space (X,mX). By using mIT -structures, we introduce and investigate a function f : (X,mIT ) → (Y,mY ) called MIT -continuous. As special cases of MIT -continuity, we obtain M -semicontinuity [21] and M -precontinuity [23].

We use Green-Riefel machinary to induce representations from a closed subgroupoid crossed product to the groupoid crossed product with a lower semicontinuous bundle of C∗-algebras .