In this note we present a new treatment of the pointfree version of the semicontinuous quasi-uniformity based on the new tool of the ring of arbitrary (not necessarily continuous) real-valued functions made available recently by J. Gutiérrez Garćıa, T. Kubiak and J. Picado [Localic real functions: a general setting, Journal of Pure and Applied Algebra 213 (2009) 1064-1074]. The purpose is to sh...

In this paper we prove existence and multiplicity results of unbounded critical points for a general class of weakly lower semicontinuous functionals. We will apply a nonsmooth critical point theory developed in [10, 12, 13] and applied in [8, 9, 20] to treat the case of continuous functionals.

We present in this paper the advantages of using the model of Euclidean paths for the geometrical analysis of a discrete curve. The Euclidean paths are a semi-continuous representation of a discrete path providing a good approximation of the underlying real curve. We describe the use of this model to obtain accurate estimations of lenght, tangent orientation and curvature.

We show that a theorem of Shchepin and Repovš concerning the smoothness of compacta follows from the theory of semicontinuous relations.

We consider the upper semicontinuity of the global random attractors for the stochastic three-component reversible Gray–Scott system on unbounded domains when the intensity of the noise converges to zero. 2013 Elsevier Inc. All rights reserved.

We introduce the concepts of IVF m-semiopen sets, IVF m-preopen sets, IVF m-semicontinuous mappings and IVF mprecontinuous mappings on interval-valued fuzzy minimal spaces. We investigate characterizations of IVF m-semicontinuous mappings and IVF m-precontinuous mappings and study properties of IVF m-semiopen sets and IVF m-preopen sets.

In this paper, we establish sufficient conditions for the existence of solutions of equilibrium problems in a metric space, that do not involve any convexity assumption either for the domain or for the function. To prove these results, a weak notion of semicontinuity is considered. Furthermore, some existence results for systems of equilibrium problems are provided.

A number of semicontinuity concepts and the relations between them are discussed. Characterizations are given for when the (set-valued) metric projection P M onto a proximinal subspace M of a normed linear space X is approximate lower semicontinuous or 2-lower semicontinuous. A geometric characterization is given of those normed linear spaces X such that the metric projection onto every one-dim...

Flesch et al [3] showed that, if the payoff functions are bounded and lower semicontinuous, then such a game always has a pure, subgame perfect -equilibrium for > 0. Here we prove the same result for bounded, upper semicontinuous payoffs. Moreover, Example 3 in Solan and Vieille [7] shows that if one player has a lower semicontinuous payoff and another player has an upper semicontinuous payoff,...