Let K be a compact Hausdorff space and C(K) the Banach space of all real-valued continuous functions on K , with the sup-norm. Types over C(K) (in the sense of Krivine and Maurey) can be uniquely represented by pairs ( ,u) of bounded real-valued functions on K , where is lower semicontinuous, u is upper semicontinuous, ≤ u, and (x) = u(x) for all isolated points x of K . A condition that charac...

We develop a framework for studying dynamical properties of hybrid systems based on considering the space of all possible trajectories of the system. In this way it is possible to treat both nondeterministic systems and systems for which the evolution does not depend continuously on the initial conditions. We show that the trajectory space is compact for the class of upper-semicontinuous hybrid...

In a previous paper, we proposed an axiomatic model for measuring self-contradiction in the framework of Atanassov fuzzy sets. This way, contradiction measures that are semicontinuous and completely semicontinuous, from both below and above, were defined. Although some examples were given, the problem of finding families of functions satisfying the different axioms remained open. The purpose of...

for all x, y ∈ X and all natural numbers n, where φn : [0,∞)→ [0,∞) and limn→∞φn = φ, uniformly on any bounded interval [0,b]. Suppose that φ is upper semicontinuous and that φ(t) < t for all t > 0. Furthermore, suppose that there exists a positive integer n∗ such that φn∗ is upper semicontinuous and φn∗(0)= 0. If there exists x0 ∈ X which has a bounded orbit O(x0)= {x0,Tx0,T2x0, . . .}, then T...