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Mar
31
comment Why is this entangled circle not a retract of the solid torus?
@Ryan: Thanks for the hint, I'll look into it!
Mar
31
comment Why is this entangled circle not a retract of the solid torus?
@Chris: Thanks for pointing it out, that was a typo, I'm sorry!
Mar
31
comment Why is this entangled circle not a retract of the solid torus?
@Theo: Thanks for adding the picture.
Mar
31
comment Why is this entangled circle not a retract of the solid torus?
The circle on the picture is entangled (?) and it goes around the hole of the donut so that it cannot be shrunk to a point.
Mar
31
asked Why is this entangled circle not a retract of the solid torus?
Mar
30
accepted Difference between linear map and homomorphism
Mar
30
comment Difference between linear map and homomorphism
thank you so much! Now I even learnt more than I asked for, e.g. I didn't know there was such a thing as a homomorphism between topological spaces. In fact, I tried to look it up on Wikipedia after reading your answer but it's not mentioned there. So a continuous function between top. spaces can also be called homomorphism!
Mar
30
comment Difference between linear map and homomorphism
@Derek: yes, you're right! Thanks for pointing out that I cannot treat an arbitrary group as a one dimensional vector space.
Mar
30
revised about continuous functions
added 3 characters in body
Mar
30
comment about continuous functions
@leopard: that's good! we're always here to help.
Mar
30
asked Difference between linear map and homomorphism
Mar
30
comment Question about notation / terminology
Many thanks! I have another question: what is the exact difference between $GL(E)$, the isomorphisms form $E$ to $E$ and $GL(n,k)$, the invertible $n \times n$ matrices with coefficients in $k$? (assuming $E$ is a vector space over $k$). Aren't invertible matrices automorphisms? And can I not write any linear automorphism as a matrix?
Mar
29
comment Largest eigenvalue of a real symmetric matrix
@Rafael: According to Wikipedia, the spectral theorem gives you conditions under which a matrix is diagonalizable, so yes, I think the spectral theorem is related.
Mar
29
revised Largest eigenvalue of a real symmetric matrix
Second hint added.
Mar
29
answered Largest eigenvalue of a real symmetric matrix
Mar
28
comment Question about notation / terminology
@Arturo: confusingly not the set of continuous functions, even though $C$ is used. But I don't think it's a typo in the script, the script is rather typo-free.
Mar
28
comment Question about notation / terminology
@Arturo: the set of functions from $G$, a group, to $k$, a field.
Mar
28
comment Question about notation / terminology
@BBischof: Sure, what would you suggest?
Mar
28
comment about continuous functions
"that delta gives you an epsilon" should be "that epsilon gives you a delta", if you would like to use the conventional notation.
Mar
28
answered about continuous functions