We are mainly concerned with some special kinds of semicontinuous domains and relationships between them. New concepts of strongly semicontinuous domains, meet semicontinuous domains and semi-FS domains are introduced. It is shown that a dcpo L is strongly semicontinuous if and only if L is semicontinuous and meet semicontinuous. It is proved that semi-FS domains are strongly semicontinuous. So...

In this paper, we introduce the concept of fuzzy almost strongly (r, s)-semicontinuous mappings on intuitionistic fuzzy topological spaces in Šostak’s sense. The relationships among fuzzy strongly (r, s)-semicontinuous, fuzzy almost (r, s)continuous, fuzzy almost (r, s)-semicontinuous, and fuzzy almost strongly (r, s)-semicontinuous mappings are discussed. The characterization for the fuzzy alm...

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 extend some topologies on the space of upper semicontinuous functions with compact support to those on that of general upper semicontinuous functions and see that graphical topology and modified L topology are the same. We then define random upper semicontinuous functions using their topological Borel field and finally give a Choquet theorem for random upper semicontinuous functions.

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...

Katětov-Tong insertion type theorem For every upper semicontinuous real function f and lower semicontinuous real function g satisfying f ≤ g, there exists a continuous real function h such that f ≤ h ≤ g (Katětov 1951, Tong 1952). For every lower semicontinuous real function f and upper semicontinuous real function g satisfying f ≤ g, there exists a continuous real function h such that f ≤ h ≤ ...

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,...

gC(μ) := { F0(C) Fμ(C) if Fμ(C) > 0 ; +∞ if Fμ(C) = 0. Then fC is an upper semicontinuous function: if μ ∈ SM is such that Fμ(C) > 0, then fC is continuous at point μ. Otherwise, fC(μ) = ∞ and fC is trivially upper semicontinuous at point μ. Clearly, one has G(μ) = infC∈C fC(μ) ; as an infimum of upper semicontinuous functions, it is itself upper semicontinuous, and therefore attains its maximu...

Using the method of generic continuity of set-valued mappings, this paper studies the stability of weakly Pareto-Nash and Pareto-Nash equilibria for multiobjective population games, when payoff functions are perturbed. More precisely, the paper investigates the continuity properties of the set of weakly Pareto-Nash equilibria and that of the set of Pareto-Nash equilibria under sufficiently smal...

In the paper we study the continuity properties of the solution set of upper semicontinuous differential inclusions in both regularly and singularly perturbed case. Using a kind of dissipative type of conditions introduced in [1] we obtain lower semicontinuous dependence of the solution sets. Moreover new existence result for lower semicontinuous differential inclusions is proved.