# Questions tagged [topological-semigroups]

A semigroup that is simultaneously a topological space, and whose semigroup operation is continuous.

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### A question about Semiflow on $[0, 1]$

Let $(T, [0, 1])$ be a semiflow, it means that $T$ is topological semigroup and $e\in T$, $t:[0, 1]\to [0, 1]$ is a continuous map for all $t\in T$, $t_0(t_1 x)= (t_0t_1)x$ for all $t_0, t_1\in T$ ...
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### A dense orbit of semiflow $(T, X)$ on $X=\{0\}\cup \{\frac{1}{n}: n=1, 2, \ldots \}$

Let $X=\{\frac{1}{n}: n\in\mathbb{N}\} \cup \{0\}$ be subspace of $\mathbb{R}$ with usual metric and let $(T, X)$ be a semiflow on $X$, this means that $\varphi:T\times X\to X$ with $\varphi(t, x)= tx$...
1 vote
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### What conditions on topological semigroup $T$ implies that if $t_n\to \infty$, then $st_n\to\infty$ for all $s\in T$?

Let $T$ be a topological semigroup. For a net $\{t_i\}$ in $T$, $t_i\to \infty$ is to mean that the net $\{t_i\}$ is ultimately outside each element of compact set $K$ in $T$. In my research, I need ...
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### A question about syndetic-preserving by subgroups

Let $T$ be a topological discrete semigroup and $S\leq T$ be a subgroup of $T$ which is closed set in $T$. For $A\subseteq S$ there is a finite set $K$ in $T$ such that $T=KA$. Is there a subset $K_0$ ...
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### Is it true that if $\{F_n\}$ is a Folner net, then $\{F_nx_n\}$ is Folner net?

Let $T$ be a right cancelative semigroup and let $\mathcal{F}=\{F_n\}_{n\in D}$ be a net in $\mathcal{P}_f(T)= \{A: A \text{ is finite subsets of } T\}$. $\mathcal{F}$ is called a Folner net if for ...
1 vote
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1 vote
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### For entourage $U$ and continuous map $t:X\to X$, is there an entourage $V$ with $t^{-1}V[x]\subseteq U[x]$?

Let $(X, \mathcal{U})$ be a uniform space, $T$ be a topological semigroup and $(T, X)$ be a semiflow. This means that $t:X\to X$ is continuous and $(t_0t_1)(x)=t_0(t_1x)$ and if $e\in T$, then $ex=x$. ...
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If $a$ and $b$ are elements of finite order in the same or in different semigroups, the $\langle a\rangle \simeq \langle b \rangle$ if and only if $a$ and $b$ have the same index and period. $\... • 494 1 vote 2 answers 43 views ### Invariance of syndetic set in topological semigroup Let$T$be a topological semigroup.$A\subseteq T$is syndetic, if there is compact set$K\subseteq T$with$T=KA$. Let syndetic set$A\subseteq T$and$g\in T$be given. I think that$Ag^{-1}=\{y: ...
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Suppose $X$ is a metric space, and let $X^*$ denote the free monoid on $X$, that is the monoid consisting of all finite strings of elements of $X$, with string concatenation as the monoid operation (...
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### Particular property of an open subsemigroup in a given topological group

In chapter $\rm{III}$ of the "Topologie générale" of Bourbaki -- which is the chapter they dedicate to a brief introduction to generalities concerning topological groups -- I have ...
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### Topological nature of IEEE floating-point numbers

If IEEE floating-point numbers had countably infinite precisions, its domain would be: $$\{-\infty\}\cup\mathbb{R}^-\cup\{-0,+0\}\cup\mathbb{R}^+\cup\{+\infty\}\cup\{\text{NaN}\}$$ Let's denote ...
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### What is an involutorial homeomorphism?

Having searched the term "involutorial" here, on Google, and in the references of the source paper where I first have met this term (in fact the only time), I am wondering whether could anyone give a ...
1 vote
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### Is there a typo in the theorem?

I have downloaded an article of A.D. Wallace named The Structure of Topological Semigroups, https://projecteuclid.org/euclid.bams/1183519418. Theorem 2.1 in the text reads: "Each subgroup of $S$ ...