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@ -154,14 +154,15 @@ By Zorn's lemma, this will follow from
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Then there is another factor $(Z,T)$ of $(X,T)$
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which is a proper isometric extension of $Y$.
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% https://q.uiver.app/#q=WzAsMyxbMiwwLCIoWCxUKSJdLFswLDAsIihZLFQpIl0sWzEsMSwiKFosVCkiXSxbMSwwXSxbMiwwXSxbMSwyLCJcXHRleHR7aXNvbWV0cmljIGV4dGVuc2lvbn0iLDFdXQ==
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% https://q.uiver.app/#q=WzAsMyxbMiwwLCIoWCxUKSJdLFswLDAsIihZLFQpIl0sWzEsMSwiKFosVCkiXSxbMCwxXSxbMCwyXSxbMiwxLCJcXHRleHR7aXNvbWV0cmljIGV4dGVuc2lvbn0iLDFdXQ==
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\[\begin{tikzcd}
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{(Y,T)} && {(X,T)} \\
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& {(Z,T)}
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\arrow[from=1-1, to=1-3]
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\arrow[from=2-2, to=1-3]
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\arrow["{\text{isometric extension}}"{description}, from=1-1, to=2-2]
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\arrow[from=1-3, to=1-1]
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\arrow[from=1-3, to=2-2]
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\arrow["{\text{isometric extension}}"{description}, from=2-2, to=1-1]
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\end{tikzcd}\]
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\end{theorem}
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\yaref{thm:furstenberg} allows us to talk about ranks of distal minimal flows:
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\begin{definition}[{\cite[{}13.1]{Furstenberg}}]
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