we characterize the rational subsets of a finite group and discuss the relations to integral cayley graphs.

We present a result which is obtained by combining a result of Carlson with the Finitary Dual Ramsey Theorem of Graham-Rothschild. We start by introducing some notation. We conform to the usual practice of identifying the least infinite ordinal ω with the set of non-negative integers. Given α, β ≤ ω, a partition of α into β blocks is an onto function X : α→ β such that min ( X−1({n}) ) < min ( ...

Abstract We show that, given a compact minimal system $(X,g)$ and an element h of the topological full group $\tau [g]$ g , infinite orbits admit locally constant orientation with respect to . use this obtain clopen partition $(X,G)$ into periodic parts, where G is any virtually polycyclic subgroup also give refinement index map describe role in submonoid generated by induced transformations Fi...

A Dowker space (that is, a normal space that is not countably metacompact) is constructed which is also screenable and the countable union of discrete subspaces. The construction and proofs are easy modifications of the ones for Balogh’s screenable Dowker space [B1]. Balogh’s example is presented alongside the modification in a new exposition with several new results common to the two spaces, i...

Introduction: Quantitative evaluation is recommended to improve diagnostic ability and serial assessment of dopamine transporter (DAT) density scans. We decided to compare the ordered subsets expectation-maximization (OSEM) with filtered back-projection (FBP), and to investigate the impact of different iteration and cut-off frequencies on SBR values. Methods</stro...

We prove that the Kleene-Kreisel space N N does not satisfy Normann’s condition. A topological space X is said to fulfil Normann’s condition, if every functionally closed subset of X is an intersection of clopen sets. The investigation of this property is motivated by its strong relationship to a problem in Computable Analysis. D. Normann has proved that in order to establish non-coincidence of...

Given a local homeomorphism σ : U → X where U ⊆ X is clopen and X is a compact and Hausdorff topological space, we obtain the possible transfer operators Lρ which may occur for α : C(X) → C(U) given by α(f) = f ◦ σ. We obtain examples of partial dynamical systems (XA, σA) such that the construction of the covariance algebra C (XA, σA) and the crossed product by partial endomorphism O(XA, α, L) ...

We continue our study of open and closed languages. We investigate how the properties of being open and closed are preserved under concatenation. We investigate analogues, in formal languages, of the separation axioms in topological spaces; one of our main results is that there is a clopen partition separating two words if and only if the words commute. We show that we can decide in quadratic t...

In a previous paper, the author considered several conditions for effective zero-dimensionality of a computable metric space X; each of the (classically equivalent) properties of having vanishing small or large inductive dimension, or covering dimension, or having a countable basis of clopen sets, can be interpreted as multi-valued operations, and the computability of these operations was shown...

This paper is a continuation of the papers [5, 6] and also of [3, 4]. In it we prove some new Stone-type duality theorems for some subcategories of the category ZLC of locally compact zero-dimensional Hausdorff spaces and continuous maps. These theorems are new even in the compact case. They concern the cofull subcategories SkeZLC, QPZLC, OZLC and OPZLC of the category ZLC determined, respectiv...