MHB Set equality with a function and its inverse.

OhMyMarkov
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Is $F^{-1}(F(E))\cap E=E$?

Thanks!
 
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OhMyMarkov said:
Is $F^{-1}(F(E))\cap E=E$?

It is always the case that $E\subseteq F^{-1}(F(E))$
 
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Plato said:
It is always the case that $E\subseteq F^{-1}(F(E))$

Yes...
 

Thread '2-sphere intrinsic definition by gluing disks' boundaries'

A sphere as topological manifold can be defined by gluing together the boundary of two disk. Basically one starts assigning each disk the subspace topology from ##\mathbb R^2## and then taking the quotient topology obtained by gluing their boundaries. Starting from the above definition of 2-sphere as topological manifold, shows that it is homeomorphic to the "embedded" sphere understood as subset of ##\mathbb R^3## in the subspace topology.
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