We detect topological semigroups that are topological paragroups, i.e., are isomorphic to a Rees product [X × H × Y ]σ of a topological group H over topological spaces X, Y with a continuous sandwich function σ : Y × X → H. We prove that a simple topological semigroup S is a topological paragroup if one of the following conditions is satisfied: (1) S is completely simple and the maximal subgrou...

We characterize the weak almost periodicity of a vector-valued, bounded, continuous function. We show that if the range of the function is relatively weakly compact, then the relative weak compactness of its right orbit is equivalent to that of its left orbit. At the same time, we give the function some other equivalent properties. 1. Introduction. Let S be a semitopological semigroup, let ᐄ be...

We detect topological semigroups that are topological paragroups, i.e., are isomorphic to a Rees product [X × H × Y ]σ of a topological group H over topological spaces X, Y with a continuous sandwich function σ : Y × X → H. We prove that a simple topological semigroup S is a topological paragroup if one of the following conditions is satisfied: (1) S is completely simple and the maximal subgrou...

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...

The classical theory of dynamical systems arose in the context of the study of di erential equations. In recent years the study of these systems has been extended beyond discrete or continuous (real) phase groups or semigroups to the theory of ows of more general topological groups or semigroups. Let S be a semitopological semigroup, not necessarily discrete. An action of S on a compact phase s...

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...

Let $\boldsymbol{B}_{\omega}^{\mathscr{F}}$ be the bicyclic semigroup extension for family $\mathscr{F}$ of ${\omega}$-closed subsets $\omega$ which is introduced in \cite{Gutik-Mykhalenych=2020}.We study topologizations inductive $\omega$. We generalize Eberhart-Selden and Bertman-West results about \cite{Bertman-West-1976, Eberhart-Selden=1969} show that every Hausdorff shift-continuous topol...

In this paper, by considering the notion of upsets we construct some topologies on BLalgebras. We show that any BL-algebras with respect to these topologies formes semitopological BLalgebra. Then we obtain some of the topological aspects of theses structures such as connectivity and compactness. Moreover, we introduced two kinds of semitopological MV -algebra by using two kinds of definition of...