# Matt N.

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 Jun7 comment Find the minimum distance that equal maximum inner product Is there a condition missing or am I misunderstanding something? Jun7 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 $0$. Jun7 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? Jun7 comment How to prove uniform continuity problem! @SwapnilTri Thank you for your kind words : ) Jun7 awarded Notable Question Jun6 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? Jun4 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. Jun4 revised What does it mean to say that a forcing “collapses cardinals”? edited tags Jun4 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. Jun4 revised Dual of $L^1$ when measure is the counting measure edited tags; edited title Jun4 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. Jun4 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 $X$? Jun4 comment A question on countability of isolated points of a subset of R @Seirios Oops, you are right. Thank you for your reply. Jun3 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 $\phi(x) = q$. Jun3 awarded Nice Question Jun2 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. Jun2 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. Jun2 comment Necessary conditions for $A=K+\operatorname{Ker}(\phi)$ Exactly. Me neither. : ) Jun2 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 : ) Jun2 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 $A \subseteq B$.