Related papers: When is weakly almost periodic equivalent to unifo…

Let $\pi\colon T\times X\rightarrow X$ with phase map $(t,x)\mapsto tx$, denoted $(\pi,T,X)$, be a \textit{semiflow} on a compact Hausdorff space $X$ with phase semigroup $T$. If each $t\in T$ is onto, $(\pi,T,X)$ is called surjective; and…

In topological dynamics, the dynamical behavior sometimes has a sharp contrast when the action is by semigroups or monoids to when the action is by groups. In this article we bring out this contrast while discussing the equivalence of…

An action of a group $G$ on a compact space $X$ is called weakly almost periodic if the orbit of every continuous function on $X$ is weakly relatively compact in $C(X)$. We observe that for a topological group $G$ the following are…

Let (G,tau_G) be a topological group. We establish relationships between weakly almost periodic topologies on G coarser than tau_G, central idempotents in the weakly almost periodic compactification G^W, and certain ideals in the algebra of…

Let $T\times X\rightarrow X, (t,x)\mapsto tx$, be a topological semiflow on a topological space $X$ with phase semigroup $T$. We introduce and discuss in this paper various transitivity dynamics of $(T,X)$.

Let $H$ be a subnormal co-compact closed subgroup of a Hausdorff topological group $T$ and $X$ a compact Hausdorff space. We prove the inheritance theorem: A point of $X$ is almost periodic (a.p.) for $T\curvearrowright X$ iff it is a.p.…

Using Gottschalk's notion\,---\,weakly locally almost periodic point, we show in this paper that if $f\colon X\rightarrow X$ is a minimal continuous transformation of a compact Hausdorff space $X$ to itself, then for all entourage…

The description of almost periodic or quasiperiodic structures has a long tradition in mathematical physics, in particular since the discovery of quasicrystals in the early 80's. Frequently, the modelling of such structures leads to…

We introduce a notion of quasi-weak equivalences associated with weak-equivalences in an exact category. It gives us a delooping for (idempotent complete) exact categories and a condition that the negative $K$-group of an exact category…

A flow $(X,T)$ induces the flow $(2^X,T)$. Quasifactors are minimal subsystems of $(2^X, T)$ and hence orbit closures of almost periodic points for $(2^X, T)$. We study quasifactors via the almost periodic points for $(2^X,T)$.

We study conditions for the abstract periodic linear functional differential equation $\dot{x}=Ax+F(t)x_t+f(t)$ to have almost periodic with the same structure of frequencies as $f$. The main conditions are stated in terms of the spectrum…

This paper is devoted to problems stated by Z. Zhou and F. Li in 2009. They concern relations between almost periodic, weakly almost periodic, and quasi-weakly almost periodic points of a continuous map f and its topological entropy. The…

Let $(T,X)$ with phase mapping $(t,x)\mapsto tx$ be a semiflow on a compact $\textrm{T}_2$-space $X$ with phase semigroup $T$ such that $tX=X$ for each $t$ of $T$. An $x\in X$ is called an \textit{a.a. point} if $t_nx\to y, x_n^\prime\to…

In this paper we study almost proximal extensions of minimal flows. Let $\pi: (X,T)\rightarrow (Y,T)$ be an extension of minimal flows. $\pi$ is called an almost proximal extension if there is some $N \in \mathbb{N}$ such that the…

The paper studies different variants of almost periodicity notion. We introduce the class of eventually strongly almost periodic sequences where some suffix is strongly almost periodic (=uniformly recurrent). The class of almost periodic…

We deduce mixed quasi-norm estimates of Lebesgue types on semi-continuous convolutions between sequences and functions which may be periodic or possess a weaker form of periodicity in certain directions. In these directions, the Lebesgue…

We define recurrence for a compactly generated para-topological group $G$ acting continuously on a locally compact Hausdorff space $X$ with $\dim X=0$, and then, show that if $\overline{Gx}$ is compact for all $x\in X$, the conditions (i)…

In this paper we introduce the notion of weighted (weakly) almost periodic compactifcation of a semitopological semigroup and generalize this notion to corresponding notion for transformation semigroup.The inclusion relation and equality of…

The purpose of this paper is to find conditions for a continuous onto map $\phi\colon X\rightarrow Y$ and its induced map $\phi_*\colon\mathcal{M}^1(X)\rightarrow\mathcal{M}^1(Y)$ to be semi-open, where $X$, $Y$ are compact Hausdorff spaces…

We investigate the automorphism groups of $\aleph\_0$-categorical structures and prove that they are exactly the Roelcke precompact Polish groups. We show that the theory of a structure is stable if and only if every Roelcke uniformly…