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visits member for 1 year, 9 months
seen Oct 21 at 16:18

Just stumbling my way through math texts. Hopefully getting my PhD one of these days.


Sep
24
awarded  Autobiographer
Jul
2
awarded  Curious
Sep
26
comment Relationship between conjugacy classes and their respective centralizers?
@DonAntonio haha, of course - I guess I should have specified nontrivial!
Sep
26
comment Relationship between conjugacy classes and their respective centralizers?
@AymanHourieh Thank you, yes I am familiar with this, and wish I thought of it beforehand! But back to my original line of thinking, is there no immediate contradiction that comes from having several conjugacy classes with the same centralizer? Could you provide an example of where this is the case if not?
Sep
26
accepted Relationship between conjugacy classes and their respective centralizers?
Sep
26
comment Relationship between conjugacy classes and their respective centralizers?
@DonAntonio These exercises come before the Sylow theorems are introduced, so I figured there was a way to figure it out without them. Up until now, I have the class equation and counting formula which are what I was working with.
Sep
26
comment Relationship between conjugacy classes and their respective centralizers?
@DonAntonio Well that just means they are in the center, correct? And since there are 2, which divides 10, that's okay as far as I know.
Sep
26
asked Relationship between conjugacy classes and their respective centralizers?
Aug
9
accepted Let $ X $ be compact and let $f: X \rightarrow Y$ be a local homeomorphism. Show that for any point $y \in Y$, $f^{-1}(y)$ is a finite set.
Aug
6
comment Let $ X $ be compact and let $f: X \rightarrow Y$ be a local homeomorphism. Show that for any point $y \in Y$, $f^{-1}(y)$ is a finite set.
I think I might be confused about compactness then. A finite cover implies that there are finitely many sets that cover $X$, but how do I know that the set $f^{-1}(y)$ lies in is finite from that? I assume the local homeomorphism does something in that regard, but I'm not sure what.
Aug
6
accepted How to prove a matrix A and a linear operator T, where T is left multiplication by A, have the same characteristic values.
Aug
6
asked Let $ X $ be compact and let $f: X \rightarrow Y$ be a local homeomorphism. Show that for any point $y \in Y$, $f^{-1}(y)$ is a finite set.
Jul
31
asked How to prove a matrix A and a linear operator T, where T is left multiplication by A, have the same characteristic values.
May
4
comment Is there more than one inconsistent theory?
Thank you for your answer! I guess I need some non-classical logic experience.
May
4
accepted Is there more than one inconsistent theory?
May
4
comment Is there more than one inconsistent theory?
I was unaware that was the common logician's usage of the word theory. But your last comment was helpful since I meant a set of sentences closed under consequence.
May
4
comment Is there more than one inconsistent theory?
I thought that's what a theory was defined as, yes. I'm sorry if this is obvious. Usually we say things like "this theory is inconsistent", not this is "the" inconsistent theory.
May
4
asked Is there more than one inconsistent theory?
May
4
comment Application of Kunneth formula to chain maps (Hatcher exercise)
I did verify the chain homotopy, but I didn't think that was sufficient to show the chain map $f$ was the same as that chain homotopy. Does that get me somewhere though?
May
3
asked Application of Kunneth formula to chain maps (Hatcher exercise)