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Pietro Majer
Pietro Majer
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Suppose that S(x)$S(x)$ is a function from a compact space A$A$ to a space of sets S$S$. Suppose that there exists a map W: A->A$W: A\to A$ and S(x)\subseteq S(W(x)).$S(x)\subseteq S(W(x)).$ Does there exist a point x$x$ such that the equality holds

S(x)= S(W(x))?$$S(x)= S(W(x))$$

Suppose that S(x) is a function from a compact space A to a space of sets S. Suppose that there exists a map W: A->A and S(x)\subseteq S(W(x)). Does there exist a point x such that the equality holds

S(x)= S(W(x))?

Suppose that $S(x)$ is a function from a compact space $A$ to a space of sets $S$. Suppose that there exists a map $W: A\to A$ and $S(x)\subseteq S(W(x)).$ Does there exist a point $x$ such that the equality holds

$$S(x)= S(W(x))$$

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alberto
alberto
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maximum with respect inclusion of a function whose output are sets

Suppose that S(x) is a function from a compact space A to a space of sets S. Suppose that there exists a map W: A->A and S(x)\subseteq S(W(x)). Does there exist a point x such that the equality holds

S(x)= S(W(x))?