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Jun
7
comment Find the minimum distance that equal maximum inner product
Is there a condition missing or am I misunderstanding something?
Jun
7
comment Find the minimum distance that equal maximum inner product
Also, I'm not sure this holds. If $H=\mathbb R^2$ and $x$ is $(1,0)$, $M$ is the x-axis then the minimal distance between $x$ and the x-axis is zero but the minimal distance between points on the y-axis with $\|y\|=1$ is strictly greater than $0$.
Jun
7
comment Find the minimum distance that equal maximum inner product
What do you mean by "...LHS is $Px_0$ now how to show RHS is also $Px_0$"? I'm not being obtuse, I really don't understand. Could you elaborate a bit please?
Jun
7
comment How to prove uniform continuity problem!
@SwapnilTri Thank you for your kind words : )
Jun
7
awarded  Notable Question
Jun
6
comment Necessary conditions for $A=K+\operatorname{Ker}(\phi)$
@tomasz Yes but your first comment implies that my first comment does not pertain. Now I am thinking that it does: if you can apply the splitting lemma it is a possible answer to the question. No?
Jun
4
comment What does it mean to say that a forcing “collapses cardinals”?
@ArthurFischer Yes, that's what I meant. Thank you for your comment. : ) But I'm still confused how this implies that some cardinals are no longer cardinals in the extension.
Jun
4
revised What does it mean to say that a forcing “collapses cardinals”?
edited tags
Jun
4
comment What does it mean to say that a forcing “collapses cardinals”?
@AndresCaicedo I thought it meant that a cardinal will have lower cardinality in the extension.
Jun
4
revised Dual of $L^1$ when measure is the counting measure
edited tags; edited title
Jun
4
comment Necessary conditions for $A=K+\operatorname{Ker}(\phi)$
Yes, I can prove it. That is: I don't think there is much to prove especially given your answer and your comment.
Jun
4
comment Necessary conditions for $A=K+\operatorname{Ker}(\phi)$
@tomasz What's the difference between direct sum and "simple internal sum"? Doesn't $X=A \oplus B$ imply $X = A + B$ if $A,B$ are subrings of some $X$?
Jun
4
comment A question on countability of isolated points of a subset of R
@Seirios Oops, you are right. Thank you for your reply.
Jun
3
comment A question on countability of isolated points of a subset of R
I was wondering why you chose to use two rational points. Couldn't one argue that since $x$ is isolated there is an $\varepsilon$-ball such that $B(x,\varepsilon) \cap A = \{x\}$. Then there exists a rational $q$ in this ball. Define $\phi(x) = q$.
Jun
3
awarded  Nice Question
Jun
2
comment Necessary conditions for $A=K+\operatorname{Ker}(\phi)$
Thank you for your comments. I will get back to you, right now (for the next few hours) something else is keeping me from thinking about this.
Jun
2
comment Necessary conditions for $A=K+\operatorname{Ker}(\phi)$
In you answer is $R$ a commutative ring or an algebra over a field? I assume you assume $\phi: R\to K$ for some field $K$. I don't want to bother you, it's just really not 100% clear to me.
Jun
2
comment Necessary conditions for $A=K+\operatorname{Ker}(\phi)$
Exactly. Me neither. : )
Jun
2
comment Necessary conditions for $A=K+\operatorname{Ker}(\phi)$
@seaturtles Yes. But in my previous comment $a$ was an element of the algebra not the the underlying field : )
Jun
2
comment Necessary conditions for $A=K+\operatorname{Ker}(\phi)$
@seaturtles I read your previous comment as "given any algebra homo. $\phi : A \to B$ then $\phi(a) = \phi(a1) = a \phi(1) = a$". Of course, this doesn't even make sense unless $A \subseteq B$.