For a topological group G we introduce the algebra SUC(G) of strongly uniformly continuous functions. We show that SUC(G) contains the algebra WAP (G) of weakly almost periodic functions as well as the algebras LE(G) and Asp(G) of locally equicontinuous and Asplund functions respectively. For the Polish groups of order preserving homeomorphisms of the unit interval and of isometries of the Urys...

We characterize function spaces of Rees matrixsemigroups. Then we study these spaces by using the topologicaltensor product technique.

The Central Sets Theorem was introduced by H. Furstenberg and then afterwards several mathematicians have provided various versions extensions of this theorem. All these theorems deal with central sets, its origin from the algebra Stone–Čech compactification arbitrary semigroup, say βS. It can be proved that every closed subsemigroup βS is generated a filter. We will show that, under some restr...

In this paper, we introduce three notions of topological entropy a free semigroup action generated by proper maps for noncompact subsets, which extends the defined Ju et al. [13] and Ma [17]. By using one-point compactification as bridge, study relations entropies between two dynamical systems. We then skew-product transformations, particular subset, relationship upper capacity maps, transforma...

Let S be a semitopological semigroup and CB(S) denote the C∗-algebra of all bounded complex valued continuous functions on S with uniform norm. A function f ∈ CB(S) is left multiplicative continuous if and only if Tμf ∈ CB(S) for all μ in the spectrum of CB(S), where Tμf(s) = μ(Lsf) and Lsf(x) = f(sx) for each s, x ∈ S. The collection of all the left multiplicative continuous functions on S is ...

Without the restriction of metrizability, topological dynamical systems (X, 〈Ts〉s∈G) are defined and uniform recurrence and proximality are studied. Some well known results are generalized and some new results are obtained. In particular, a topological dynamical characterization of central sets in an arbitrary semigroup (G,+) is given and shown to be equivalent to the usual algebraic characteri...

A small part of real line which is very close to zero has rich combinatorial properties. The aim this paper express and then prove some locally concepts near a virtual idempotent by considering the wap -compactification semitopological semigroup id="M2"> S . id="M3"> id="M4"> , denoted id="M5"> <mro...