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 Sep24 awarded Autobiographer Jul2 awarded Curious Sep26 comment Relationship between conjugacy classes and their respective centralizers? @DonAntonio haha, of course - I guess I should have specified nontrivial! Sep26 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? Sep26 accepted Relationship between conjugacy classes and their respective centralizers? Sep26 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. Sep26 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. Sep26 asked Relationship between conjugacy classes and their respective centralizers? Aug9 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. Aug6 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. Aug6 accepted How to prove a matrix A and a linear operator T, where T is left multiplication by A, have the same characteristic values. Aug6 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. Jul31 asked How to prove a matrix A and a linear operator T, where T is left multiplication by A, have the same characteristic values. May4 comment Is there more than one inconsistent theory? Thank you for your answer! I guess I need some non-classical logic experience. May4 accepted Is there more than one inconsistent theory? May4 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. May4 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. May4 asked Is there more than one inconsistent theory? May4 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? May3 asked Application of Kunneth formula to chain maps (Hatcher exercise)