MHB Set equality with a function and its inverse.

OhMyMarkov
Messages
81
Reaction score
0
Is $F^{-1}(F(E))\cap E=E$?

Thanks!
 
Last edited by a moderator:
Physics news on Phys.org
OhMyMarkov said:
Is $F^{-1}(F(E))\cap E=E$?

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

Yes...
 

Thread 'About the definition of topological manifold using closed sets'

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.
View full post »

Similar threads

I On Borel sets of the extended reals
  • · Replies 2 ·
Replies
2
Views
2K
MHB Prove f is One-to-One: (a) and (b) | Help with Choosing Inverse Formula
  • · Replies 2 ·
Replies
2
Views
2K
I On deriving the (inverse) Fourier transform from Fourier series
  • · Replies 4 ·
Replies
4
Views
3K
I Connection between absolute continuity of function and measure
  • · Replies 2 ·
Replies
2
Views
2K
I Uniform closure of algebra of bounded functions is uniformly closed
  • · Replies 2 ·
Replies
2
Views
2K
I Is ##J(f)## Non-Zero in ##U## for a Bijective ##C^m## Function?
  • · Replies 1 ·
Replies
1
Views
2K
I Continuity and Open Sets .... Sohrab, Theorem 4.3.4 .... ....
  • · Replies 3 ·
Replies
3
Views
2K
I A concise "proof" of the Riemann-Lebesgue lemma
  • · Replies 1 ·
Replies
1
Views
2K
I Continuity of an inverse of a function
  • · Replies 2 ·
Replies
2
Views
2K
I Continuity of linear map from subspace of Euclidean space
  • · Replies 2 ·
Replies
2
Views
1K