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The cardinal characteristic $\mathfrak r_{(X,f)}$ of a dynamical system

I am interested in a "dynamical" modification of the cardinals $\mathfrak r$ and $\mathfrak r_\sigma$, well-known in the theory of cardinal characteristics of the continuum. For a compact ...
Taras Banakh's user avatar
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1 vote
1 answer
136 views

A permutation group inducing a topologically transitive action without dense orbits on $\omega^*$

Let $G$ be a subgroup of the permutation group $S_\omega$ of the countable infinite set $\omega$. Each bijection $g\in G$ admits a unique extension to a homeomorphism $\bar g$ of the Stone-Cech ...
Taras Banakh's user avatar
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5 votes
1 answer
524 views

A topologically transitive dynamical system without dense orbits

By a dynamical system I understand a pair $(K,G)$ consisting a compact Hausdorff space and a subgroup $G$ of the homeomorphism group of $K$. We say that a dynamical system $(K,G)$ $\bullet$ is ...
Taras Banakh's user avatar
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5 votes
2 answers
655 views

$C^n$ And Forcing: Reading a Recent Paper By Kunen

While reading a recent paper by Kunen arxiv.org/abs/0912.3733, which deals with PFA and the existence of certain differentiable functions, (defined on all of $\mathbb{R}$) which map certain $\aleph_1$-...
Not Mike's user avatar
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