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

A polyadic space is a Hausdorff continuous image of some power of the onepoint compactification of a discrete space. We prove a Ramsey-like property for polyadic spaces which for Boolean spaces can be stated as follows: every uncountable clopen collection contains an uncountable subcollection which is either linked or disjoint. One corollary is that (ακ) is not a universal preimage for uniform ...

Sets and Intervals • An interval with round brackets such as (a, b) means all the numbers between a and b not including a and b. We call this interval an open interval. • An interval with square brackets such as [a, b] means all the numbers between a and b including a and b. We call this interval a closed interval. • An interval with one square bracket and one closed bracket is called a clopen ...

Geschke proved in [2] that there is a clopen graph on \(2^\omega \) which 3-saturated, but the graphs do not even have infinite subgraphs are 4-saturated; however \(F_\sigma \(\omega _1\)-saturated. It turns out no closed \)-saturated, see [3]. In this note we complete picture by proving for every \(n\in {\mathbb {N}}\) an n-saturated Cantor space \). The key lemma based probabilistic argument....

human brucellosis is a major health problem in developing countries. a number of patients with human brucellosis do not recover from the acute stage of the disease and pass into the chronic form. since the pathophysiology of this change is not well understood, we studied the t-cell subsets during the acute, subacute and chronic forms of human brucellosis. in this study we found alterations in t...

In this paper, our purpose is twofold. Firstly, the tensor andresiduum operations on $L-$nested systems are introduced under thecondition of complete residuated lattice. Then we show that$L-$nested systems form a complete residuated lattice, which isprecisely the classical isomorphic object of complete residuatedpower set lattice. Thus the new representation theorem of$L-$subsets on complete re...

In this paper, we construct two fuzzy sets using the notions of level subsets and strong level subsets of a given fuzzy set in a ring R. These fuzzy sets turn out to be identical and provide a universal construction of a fuzzy ideal generated by a given fuzzy set in a ring. Using this construction and employing the technique of strong level subsets, we provide the shortest and direct fuzzy set ...

In [3], Brodhead, Downey and Ng introduced some new variations of the notions of being Martin-Löf random where the tests are all clopen sets. We explore the lowness notions associated with these randomness notions. While these bounded notions seem far from classical notions with infinite tests like Martin-Löf and Demuth randomness, the lowness notions associated with bounded randomness turn out...

The present paper is mainly concerned with establishing conditions which .assure that all lattice regular measures have additional smoothness properties or that simply all two-valued such measures have such properties and are therefore Dirac measures. These conditions are expressed in terms of the general Wallman space. The general results are then applied to specific topological lattices, yiel...

10.2. Example We consider the abstract dynamical system given in 9.18: the shift system over S where the phase space X is the product space {1, . . . , r}, for some r ≥ 2. For any R ⊆ S, there are x and U such that R(x, U) = R: simply pick x ∈ X be such that x(s) = 1 iff s ∈ R; so x might be considered as a characteristic function of R. Put U = {z ∈ X : z(1S) = 1}, a clopen subset of X. Then fo...