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Martin Sleziak
Martin Sleziak
2:22 AM
1
Q: Connections between Ext and vertex

RhythmInkI haven't gotten a chance to search through the literature yet, but I was wondering if anyone knows anything about or has any thoughts about this idea: So, if we have a module $M$, then we can easily talk about $Ext^n_R(M,N)$ and we know that if $M$ is projective that $Ext^n(M,N)=0$ for all $n \...

representation-theory homological-algebra local-representation-theory
 
 
16 hours later…
Martin Sleziak
Martin Sleziak
6:52 PM
new-tag A new tag sard-theorem was created by HK Lee.
0
Q: $f : \mathbb{S}^1\rightarrow \mathbb{S}^2$ is not onto.

HK Lee Question : $f : \mathbb{S}^1\rightarrow \mathbb{S}^2$ is a continuous map s.t. for almost all $x\in \mathbb{S}^1$ in Lebesgue measure, there is an open ball $B(x,\delta)$ s.t. $f|B(x,\delta)$ is a rectifiable path. Then $f$ is not a onto map. How can we prove this ? Remark : (1) There is a ...

general-topology sard-theorem
Sard's theorem
Sard's theorem, also known as Sard's lemma or the Morse–Sard theorem, is a result in mathematical analysis that asserts that the set of critical values (that is, the image of the set of critical points) of a smooth function f from one Euclidean space or manifold to another is a null set, i.e., it has Lebesgue measure 0. This makes the set of critical values "small" in the sense of a generic property. The theorem is named for Anthony Morse and Arthur Sard. == Statement == More explicitly (Sternberg (1964, Theorem II.3.1); Sard (1942)), let f : ...
 

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