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FINITE SETS WITH FAKE OBSERVABLE CARDINALITY
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 Title & Authors
FINITE SETS WITH FAKE OBSERVABLE CARDINALITY
Artigue, Alfonso;
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 Abstract
Let X be a compact metric space and let |A| denote the cardinality of a set A. We prove that if is a homeomorphism and , then for all > 0 there is such that |A| = 4 and for all there are , , such that dist(x, y) < . An observer that can only distinguish two points if their distance is grater than , 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 hyperexpansive homeomorphisms the same -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.
 Keywords
topological dynamics;expansive homeomorphisms;
 Language
English
 Cited by
1.
Levels of Generalized Expansiveness, Journal of Dynamics and Differential Equations, 2017, 29, 3, 877  crossref(new windwow)
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