469 reputation
18
bio website users.muohio.edu/mckennp2
location
age
visits member for 1 year, 3 months
seen yesterday

Visiting assistant professor at Miami University of Ohio.


Apr
3
answered Different definitions of P-Points (ultrafilters)
Mar
17
comment There exists a unique isomorphism between wosets
@AsafKaragila: Are you saying it's too much of a hint, or that I should have posted it as an answer instead of a comment?
Mar
17
comment Why is $\beta \omega$ compact?
Hint (for the compactness part): Consider a family $\mathcal{F}$ of sets $A\subset\omega$. Find a condition on $\mathcal{F}$ which is equivalent to the assertion that the $\hat{A}$'s form a cover of $\beta\omega$.
Mar
12
comment There exists a unique isomorphism between wosets
Hint: remember that $f$ and $g$ are order-isomorphisms. This means that they are not only order-preserving, but bijective as well.
Feb
17
comment Various Definitions of Direct Integrals
Have you looked at Dixmier's book?
Feb
17
comment Can we find an invertible projection in an arbitrary von Neumann algebra?
The spectrum of any projection in a C*-algebra is contained in $\{0,1\}$. If it's invertible, then the spectrum is only $\{1\}$. The spectral theorem then implies that such a projection is just the identity.
Jan
6
comment $f:P(X)\to X$ property
That works, thanks!
Jan
6
comment $f:P(X)\to X$ property
can you elaborate on why $B$ is nonstationary at the end?
Dec
29
comment A topological property of shapes like $\bot$ in $\Bbb{R}^2$
@Stahl: I don't think that works. Let $v_1,v_2,v_3$ be the endpoints of the three branches (with corresponding labels) and consider a path $p : [0,1]\to X$ traveling from $v_1$ to $v_3$, crossing the center point at $t = 1/2$. With your choice of $f$, we have $f(p(t),v_2) = p(t)$ whenever $t \le 1/2$, but $f(p(t),v_2) = v_2$ whenever $t > 1/2$.
Dec
27
answered nonsurjectivity of Banach-Stone theorem
Dec
27
comment Examples of loops which have two-sided inverses.
It looks like the unit octonions form a finite example.
Dec
22
awarded  Yearling
Sep
23
answered Independent families versus generators in boolean algebras
Sep
4
asked Independent families versus generators in boolean algebras
Aug
9
asked Is the class of countable posets well-quasi-ordered by embeddability?
May
15
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)?
Apr
29
comment characters of a $C^*$-algebra
This is great, thanks Martin!
Apr
29
accepted characters of a $C^*$-algebra
Apr
26
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.
Apr
26
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.