Let fig be the Stone-Cech compactification of a group G, Aa the set of all almost periodic points in G, Ka c[U { supp eLIM(G)}] and Ra the set of all recurrent points in fiG. In this paper we will study the relationships between Ka and Ra, and between Aa and Ra. We will show that for any infinite elementary amenable group G, Aa Ra and RaKa =/= .

Let $S$ be a dense subsemigroup of $(0,+infty)$. In this paper, we state   definition of thick near zero, and also  we will introduce a definition that is equivalent to the definition of piecewise syndetic near zero which presented by Hindman  and Leader in [6].  We define density near zero for subsets of $S$ by a collection of nonempty finite subsets of $S$ and we investigate the conditions un...

If p : E → B is a continuous surjection between completely regular spaces E and B, we may apply the Stone-Čech compactification functor β to obtain a surjection βp : βE → βB. It is well-known that if E = B × F where F is a finite set and p is projection on the first factor, then βE = βB × βF , and βp is again projection on the first factor. In this paper, we apply β to an n-fold covering map, t...

In this paper, new methods for analyzing models of weak subsystems Peano Arithmetic are proposed. The focus will be on the study algebro-combinatoric properties certain definable cuts. Their relationship with segments that satisfy more induction, those limited by standard powers/roots an element, and also sets in Bounded Induction is studied. As a consequence, some considerations Π 1 -interpret...

This paper represents a continuation of our programme [16, 13] of extending various concepts of general topology from the setting of Hausdorff (or, at most, 7̂ ) spaces, in which they are usually embedded, to the larger classes of spaces we need to consider in the theory of computation. The topic of compactification poses an obvious challenge to this programme, since only a Tychonoff space can h...

We present two examples of nice normal spaces X having the property that for some xed-point free homeomorphism on X its Cech-Stone extension has a xed point. One of the spaces presented here is locally countable, locally compact, separable , normal, countably paracompact and weakly zero-dimensional. The other one is hereditarily normal and strongly zero-dimensional. Our construction of this exa...