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.

BACKGROUND Trichoepithelioma is a rare benign skin lesion that originates from hair follicles. Trichoepitheliomas are mostly seen in the scalp, nose, forehead, and upper lip. METHODS We present a large family of Iranian origin with 15 individuals affected with multiple familial trichoepithelioma in four generations, and treated with three different methods. RESULTS Trichoepithelioma is his...

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].