MHB Understanding Picard Iteration: What Does ${f}^{n}x \subseteq {f}^{n+1}x$ Mean?

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İn some articles...I see something... Let ${x}_{n}=T{x}^{n-1}$ be a Picard Operator...Then ${f}^{n}x \subseteq {f}^{n+1}x$...What is the meaning of this ? Can you help me ?
 
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You need to give just a bit more context, please. So far, $T$ is the Picard operator; Picard operators act on functions, so the $x_n$ are functions. But I have no idea what the $f^n$ symbols mean.
 
We all know the definition of n-dimensional topological manifold uses open sets and homeomorphisms onto the image as open set in ##\mathbb R^n##. It should be possible to reformulate the definition of n-dimensional topological manifold using closed sets on the manifold's topology and on ##\mathbb R^n## ? I'm positive for this. Perhaps the definition of smooth manifold would be problematic, though.

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