Periods of periodic points for transitive degree one maps of the circle with a fixed point.
Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators.
Piece-Wise Closed Functions.
Piece-wise Closed Functions: Corrigendum.
Poincaré and domain invariance theorem
Poincaré's recurrence theorem for set-valued dynamical systems
Abstract. The existence theorem of an invariant measure and Poincare's Recurrence Theorem are extended to set-valued dynamical systems with closed graph on a compact metric space.
Points with maximal Birkhoff average oscillation
Let be a continuous map with the specification property on a compact metric space . We introduce the notion of the maximal Birkhoff average oscillation, which is the “worst” divergence point for Birkhoff average. By constructing a kind of dynamical Moran subset, we prove that the set of points having maximal Birkhoff average oscillation is residual if it is not empty. As applications, we present the corresponding results for the Birkhoff averages for continuous functions on a repeller and locally...
Pointwise convergence and the Wadge hierarchy
We show that if is a separable metrizable space which is not -compact then , the space of bounded real-valued continuous functions on with the topology of pointwise convergence, is Borel--complete. Assuming projective determinacy we show that if is projective not -compact and is least such that is then , the space of real-valued continuous functions on with the topology of pointwise convergence, is Borel--complete. We also prove a simultaneous improvement of theorems of Christensen...
Pointwise limits of subsequences and -sets
Polars in distributive lattices with the smallest element
Positive definite functions and coincidences
Presentations of subshifts and their topological conjugacy invariants.
Preservation of the Borel class under open-LC functions
Let X be a Borel subset of the Cantor set C of additive or multiplicative class α, and f: X → Y be a continuous function onto Y ⊂ C with compact preimages of points. If the image f(U) of every clopen set U is the intersection of an open and a closed set, then Y is a Borel set of the same class α. This result generalizes similar results for open and closed functions.
Principal continuum congruences, regular ...-classes and local subsemigroups.
Problems on Periodicity - Functions and Semigroups
Productive representations of semigroups by pairs of structures
Productivity of coreflective classes of topological groups
Every nontrivial countably productive coreflective subcategory of topological linear spaces is -productive for a large cardinal (see [10]). Unlike that case, in uniform spaces for every infinite regular cardinal , there are coreflective subcategories that are -productive and not -productive (see [8]). From certain points of view, the category of topological groups lies in between those categories above and we shall show that the corresponding results on productivity of coreflective subcategories...
Products of ideals of Borel sets
Products of locally compact groups with zero and their actions.
Products of metric, uniform and topological spaces