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- W2068255451 abstract "Let $X$ be a compact metric space and let $|A|$ denote the cardinality of a set $A$. We prove that if $fcolon Xto X$ is a homeomorphism and $|X|=infty$ then for all $delta>0$ there is $Asubset X$ such that $|A|=4$ and for all $kin Z$ there are $x,yin f^k(A)$, $xneq y$, such that $dist(x,y)<delta$. An observer that can only distinguish two points if their distance is grater than $delta$, for sure will say that $A$ has at most 3 points even knowing every iterate of $A$ and that $f$ is a homeomorphism. We show that for hyper-expansive homeomorphisms the same $delta$-observer will not fail about the cardinality of $A$ if we start with $|A|=3$ instead of $4$. Generalizations of this problem are considered via what we call $(m,n)$-expansiveness." @default.
- W2068255451 created "2016-06-24" @default.
- W2068255451 creator A5019940300 @default.
- W2068255451 date "2014-04-02" @default.
- W2068255451 modified "2023-09-27" @default.
- W2068255451 title "Finite Sets with Fake Observable Cardinality" @default.
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