We consider generalizations of a well-known class of spaces, called by S. Mrówka, N ∪R, where R is an infinite maximal almost disjoint family (MADF) of countable subsets of the natural numbersN . We denote these generalizations by ψ = ψ(κ,R) for κ ≥ ω. Mrówka proved the interesting theorem that there exists an R such that |βψ(ω,R) \ ψ(ω,R)| = 1. In other words there is a unique free z-ultrafilt...

Rough set theory is a paradigm for approximate reasoning based on the assumption that concepts are divided into exact and non–exact (called also rough) ones by means of a topological structure induced by a representation of knowledge as a classification. A classification in its most simple form is an equivalence relation on a universe of objects; the classification induces a partition topology ...

We prove that there are uncountably many sets that are low for the class of Schnorr random reals. We give a purely recursion theoretic characterization of these sets and show that they all have Turing degree incomparable to 0 0. This contrasts with a result of Ku cera and Terwijn 5] on sets that are low for the class of Martin-LL of random reals. The Cantor space 2 ! is the set of innnite binar...

Throughout this paper X denotes a compact and zero-dimensional Hausdorr space. We shall be concerned with Theorem 0.1 The following assertions are equivalent. (A) X is the continuous image of a compact ordered space. (B) X is the continuous image of a zero-dimensional compact ordered space. (C) X has a T 0-separating cross-free family of clopen sets. (D) X has a T 0-separating non-Archimedian f...

A minimal subshift (X, T ) is linearly recurrent if there exists a constant K so that for each clopen set U generated by a finite word u the return time to U , with respect to T , is bounded by K|u|. We prove that given a linearly recurrent subshift (X, T ) the set of its non-periodic subshift factors is finite up to isomorphism. We also give a constructive characterization of these subshifts.

Rough sets deal with the vagueness and granularity in information systems. Reference[3] discusses rough approximations on a complete completely distributive lattice(CCD lattice for short) and brings generalizations of rough sets into a unified framework. This paper is devoted to the discussion of the relationship between approximations and topologies on a CCD lattice. It is proved that the set ...

peripheral blood t lymphocytes and their subsets were studied in 31 patients with beta thalassemia major (age 2-12years) and compared with 14 age-arid sex-matched healthy controls. three monoclonal antibodies (anti-cd3, anti cd-f, unti-cds) were simultaneously applied for detection of th (cd3-, cd4^), tsk (cd3+, cd8+) and th/ts ratio by flow-cytometry respectively. the results of this study sho...

0. Notation. The basic notation for Boolean algebras is the standard one (for instance, see [l]). Throughout this paper, the letter O will denote the two-element Boolean algebra; whenever a topology is assumed to be defined on 0, then this topology is the discrete one. If 73 is a Boolean algebra, then a valuation of B is a homomorphism from 73 onto 0. We make precise the terminology we shall be...

A charge (finitely additive measure) defined on a Boolean algebra of sets taking values in a group G is called a strictly nonzero (SNZ) charge if it takes the identity value in G only for the zero element of the Boolean algebra. A study of such charges was initiated by Rudiger Göbel and KPS Bhaskara Rao in 2002 [3]. Our main result is a solution to one of the questions posed in that paper: we s...