# Paul

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bio website math.cmu.edu/~pmckenne location age member for 5 months seen 17 hours ago profile views 40

Grad student at Carnegie Mellon University.

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 May15 comment Is $X$ pseudocompact@Paul, as written conditions (1) and (2) are contradictory. (Assuming (1), take $H = H_0$ in (2).) Did you mean to have the roles of $\alpha$ and $\beta$ switched in (1)? Apr29 comment characters of a $C^*$-algebraThis is great, thanks Martin! Apr29 accepted characters of a $C^*$-algebra Apr26 comment $f: \mathbb{R}^2 \to \mathbb{R}$ a continuous open map, show that for each $x \in \text{range}(f)$, $f^{-1}(x)$ is always uncountable.@TMM: Okay, I'll remember that in the future. Apr26 revised $f: \mathbb{R}^2 \to \mathbb{R}$ a continuous open map, show that for each $x \in \text{range}(f)$, $f^{-1}(x)$ is always uncountable.corrected the dependence of g_a on a. Apr26 comment $f: \mathbb{R}^2 \to \mathbb{R}$ a continuous open map, show that for each $x \in \text{range}(f)$, $f^{-1}(x)$ is always uncountable.I've supplied the edit. Apr26 suggested suggested edit on $f: \mathbb{R}^2 \to \mathbb{R}$ a continuous open map, show that for each $x \in \text{range}(f)$, $f^{-1}(x)$ is always uncountable. Apr26 comment $f: \mathbb{R}^2 \to \mathbb{R}$ a continuous open map, show that for each $x \in \text{range}(f)$, $f^{-1}(x)$ is always uncountable.Hagen, I don't see the dependence of $g_a$ on $a$. Is there a typo in your definition? Apr25 awarded Commentator Apr25 comment Restrictions of null/meager idealYou should post this on MO, if you haven't already. Apr25 asked characters of a $C^*$-algebra Apr3 awarded Tumbleweed Mar27 revised A map that is $(n-1)$-positive but not $n$-positiveadded 56 characters in body Mar27 comment Are all large cardinal axioms expressible in terms of elementary embeddings?Yes, my answer was based on a more literal interpretation of the OP's question; "is every large cardinal the critical point of an elementary embedding?" Mar27 asked A map that is $(n-1)$-positive but not $n$-positive Mar27 answered Are all large cardinal axioms expressible in terms of elementary embeddings? Mar26 comment When is a $*$-homomorphism between multiplier algebras strictly continuous?Thanks to Martin Sleziak for prompting me to add the answer here. Mar26 revised When is a $*$-homomorphism between multiplier algebras strictly continuous?Added an answer to the last question. Possibly more to come later. Mar13 comment Subset of a P-ideal need not be a P-ideal@Martin; perhaps it's not so easy. I've added an explanation of the construction. Mar13 revised Subset of a P-ideal need not be a P-idealAdded some explanation.