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Apr
23
comment Let $f:\mathbb{R}\to\mathbb{R}$ be a differentiable function and $C<1$ such that $|f'(x)|\le C$ for all $x$
Are you asking a different question in the title and the body?
Apr
23
revised Let $f:\mathbb{R}\to\mathbb{R}$ be a differentiable function and $C<1$ such that $|f'(x)|\le C$ for all $x$
edited title
Apr
10
comment All prime ideals are maximal - Counterexample
Can you think of an integral domain which is not a field?
Apr
8
comment Notation help abstract algebra
Yes. Please stop using all caps though.
Apr
8
comment Notation help abstract algebra
Note that $R$ needs to be an integral domain for this to make sense.
Mar
30
comment The theorem on formal functions
Taking inverse limits is a way of looking at all infinitesimal neighborhoods at once, so to me it seems like a natural thing to do, not something that muddy's the comparison.
Mar
27
comment Give an example to show that there need not exist $x\in X$ such that $\|x\|=1$ and $Lx=1$.
Ok, I fixed the answer.
Mar
27
revised Give an example to show that there need not exist $x\in X$ such that $\|x\|=1$ and $Lx=1$.
added 18 characters in body
Mar
27
comment Give an example to show that there need not exist $x\in X$ such that $\|x\|=1$ and $Lx=1$.
Yes that is what I meant by $e_i$. It spans by definition of $\mathbb{R}^\infty$.
Mar
27
comment Give an example to show that there need not exist $x\in X$ such that $\|x\|=1$ and $Lx=1$.
Sorry, I did not read "functional" carefully, you are correct that this is not a functional; it is an operator on $\mathbb{R}^\infty$. Unfortunately I am kind of busy right now but you could try to check if the example still works if we define $L$ the way you suggested. If not we could use the box norm instead and it should work.
Mar
27
revised Linear transformation that is like projection
added 144 characters in body
Mar
27
comment Linear transformation that is like projection
I have added most of the details, I hope you can fill in the rest.
Mar
27
revised Linear transformation that is like projection
added 181 characters in body
Mar
27
revised Linear transformation that is like projection
added 158 characters in body
Mar
27
comment Linear transformation that is like projection
Write $w$ as a linear combination in this basis, and apply $T$ again, to see what happens.
Mar
27
revised Linear transformation that is like projection
added 145 characters in body
Mar
27
answered Linear transformation that is like projection
Mar
27
comment Manifolds and CW-complexes
Using Morse theory one can show that a smooth manifold is homotopic to a CW complex.
Mar
27
accepted Dimension of local rings on scheme of finite type over a field.
Mar
27
answered Give an example to show that there need not exist $x\in X$ such that $\|x\|=1$ and $Lx=1$.