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 'Apparent counter-example to Cauchy-Goursat theorem (Complex Analysis)'

I posted this question on math-stackexchange but apparently I asked something stupid and I was downvoted. I still don't have an answer to my question so I hope someone in here can help me or at least explain me why I am asking something stupid. I started studying Complex Analysis and came upon the following theorem which is a direct consequence of the Cauchy-Goursat theorem: Let ##f:D\to\mathbb{C}## be an anlytic function over a simply connected region ##D##. If ##a## and ##z## are part of...
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