A dynamical version of the Bourgain-Fremlin-Talagrand dichotomy shows that the enveloping semigroup of a dynamical system is either very large and contains a topological copy of βN, or it is a “tame” topological space whose topology is determined by the convergence of sequences. In the latter case the dynamical system is called tame. We use the structure theory of minimal dynamical systems to s...

In this paper, we investigate the basic structural properties of (analytic) q-exponentially equicontinuous (a, k)-regularized C-resolvent families in sequentially complete locally convex spaces. We provide some applications in fluid dynamics, linear thermoviscoelasticity, and illustrate obtained theoretical results by several other examples. Mathematics Subject Classification: 47D03, 47D06, 47D99.

This derivation of (2) is not valid, because this duality applies to inferences and theorems only, not to definitions. In fact, (1) should be treated as an axiom. Accordingly, the duality of Lemma 3.3.1 would not be valid until the dual (2) of (1) is proved independently, as we do below. Our new proof will make use of Proposition 3.3.3, the original proof of which is based on duality. So, we mu...

Answering a recent question posed by Gregori, Morillas and Sapena (“On a class of completable fuzzy metric spaces”, Fuzzy Sets and Systems, 161 (2010), 2193–2205) we present two examples of non strong fuzzy metrics (in the sense of George and Veeramani).