We show that, in any unitary (commutative or not) Baire locally pseudoconvex algebra with a continuous product, the power maps are equicontinuous at zero if all entire functions operate. We obtain the same conclusion if every element is bounded. An immediate consequence is a result of A. Arosio on commutative and complete metrizable locally convex algebras.

We consider an asymptotic version of Mas-Colell’s theorem on the existence of pure strategy Nash equilibria in large games. Our result states that, if players’ payoff functions are selected from an equicontinuous family, then all sufficiently large games have an ε – pure, ε – equilibrium for all ε > 0. We also show that our result is equivalent to Mas-Colell’s existence theorem, implying that i...

Katznelson’s Question is a long-standing open question concerning recurrence in topological dynamics with strong historical and mathematical ties to problems combinatorics harmonic analysis. In this article, we give positive answer for certain towers of skew-product extensions equicontinuous systems, including systems the form <mml:math xmlns:mml="htt...

We obtain analogs of the results on equicontinuity families quasiregular mappings that take no values from a fixed continuum. prove these are equicontinuous whenever quasiconformality characteristics have finite mean oscillation at every inner point. In this context, we also generalized quasiisometries Riemannian manifolds.

This is the summary of a more detailed study on transformation groups on a metric phase space X, which is equicontinuous except for a set N(X) which is topologically sufficiently small compared to its complement. Kerékjartó [7] (1934) gave the following results. Let ƒ be an orientation preserving self-homeomorphism of the 2-sphere S whose powers (both positive and negative) are equicontinuous e...