Re: T^-1(T(U)) = ?
- From: Nik <nikita2.evseev@xxxxxxxxx>
- Date: Sun, 23 Sep 2007 16:21:58 -0000
On 23 , 23:07, José Carlos Santos <jcsan...@xxxxxxxx> wrote:
On 23-09-2007 16:58, Nik wrote:
Sorry. U is subset X, an T belongs to L(X;Y). But i think: let X = R
and Y = R^2 and T(x) = 0. So? U = [0,1] then T^{-1}(T(U)) = X =/=
U. ?
In this case, T does not have an inverse map. Therefore, my guess is
that when wrote, at your previous, that T^-1 is the "inverse
correspondence" of T, what you meant was that T^-1(A) is the inverse
image of A under T.
If T is injective, T^-1(T(U)) = U. Otherwise, all you can is that it
T^-1(T(U)) contains U.
Best regards,
Jose Carlos Santos
Yes. I said about T^{-1}(y) :={x from X| such as T(x) = y}, But don't
not know how correct called in english.
thanks.
.
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