Let (X, d, T ) be a dynamical system, where (X, d) is a compact metric space and T : X → X a continuous map. We introduce two conditions for the set of orbits, called respectively g-almost product property and uniform separation property. The g-almost product property holds for dynamical systems with the specification property, but also for many others. For example all β-shifts have the g-almos...

This is a talk about the development of Ramsey theory, from combinatorial results like the classical pigeon hole principle, Ramsey’s theorem [14] and Hindman’s theorem [8], making emphasis in the notion of topological Ramsey space. In [6], Ellentuck gave a characterization of the Ramsey property which gave rise to the topological Ramsey theory. It was anticipated by the works of Nash-Williams [...

The present paper studies almost fixed point property for digital spaces whose structures are induced by Marcus-Wyse (M-, for brevity) topology. In this paper we mainly deal with spaces X which are connected M-topological spaces with M-adjacency (MA-spaces or M-topological graphs for short) whose cardinalities are greater than 1. Let MAC be a category whose objects, denoted by Ob(MAC), are MA-s...

We exhibit a locally biholomorphic mapping with simply connected image, which fails to be a topological covering. Introduction In [1], A.F.Beardon shows an example of a ’covering surface’ over the unit disc D ⊂ C, which is not a topological covering. We recall that a ’covering surface’ of a regionD ⊂ C, is a Riemann surface S admitting surjective conformal mapping onto D, whereas a continuous m...

A match-to-sample shape-discrimination task was employed to measure the detectability of different types of transformations. To create the foils for this task, the standard object could be altered by adding a small hole (a topological property), adding small bumps to straight edges (a projective property), changing the relative orientations of parallel contours (an affine property), or stretchi...

We give the natural topological model for ¬BD-N, and use it to show that the closure of spaces with the anti-Specker property under product does not imply BD-N. Also, the natural topological model for ¬BD is presented. Finally, for some of the realizability models known indirectly to falsify BD-N, it is brought out in detail how BD-N fails. keywords: anti-Specker, BD, BD-N, realizability, topol...