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olivier dot begassat dot cours at gmail dot com


Jan
19
comment Mapping torus with homotopic homeomorphisms
I don't know to be honest, but it seems like a good condition to impose.
Jan
19
comment Mapping torus with homotopic homeomorphisms
I mean a homotopy $H:X\times[0,1]\to X$ such that for all $t$, $H_t$ is a homeomorphism of $X$. In the case of the identity and the antipodal map of the sphere, you can take the homotopy $H(z,t)=e^{it\pi}z$, which is a homotopy through homeomorphisms.
Jan
19
comment Mapping torus with homotopic homeomorphisms
They are homotopic through homeomorphisms though. This is more restrictive than simply being homotopic in general. Do you see why the example I gave in my previous comment is a counter example?
Jan
19
comment Mapping torus with homotopic homeomorphisms
Do you mean simply homotopic or homotopic through homeomorphisms? In the first case the answer is no, take for instance $X=[0,1]$ and $f=\mathrm{id}$ and $g=1-\mathrm{id}$.
Jan
19
comment How can I show $U^{\bot \bot}\subseteq \overline{U}$?
This requires the Hilbert projection theorem mentioned in the previous answer.
Jan
18
comment $(2n-1)$-form is closed
You are expected to show your work! Have you tried applying brute force, i.e. doing the calculation? It's not that hard to calculate $d\Omega$ directly...
Jan
18
comment Property of $ L^p( [0,T] , X) $ with X Banach space
Google "Banach space valued Lp functions", you'll find several basic references. The name attached to this field seems to be "Bochner integral" and "vector valued $L^p$ space".
Jan
18
comment Compact subset of space of matrices and compactness verification of a set of eigenvalues
@RobertGreen Thank you! that's very gracious : )
Jan
18
revised Compact subset of space of matrices and compactness verification of a set of eigenvalues
deleted 143 characters in body
Jan
18
answered Compact subset of space of matrices and compactness verification of a set of eigenvalues
Jan
18
comment Takhtajan's “Quantum Mechanics for Mathematicians”
I think this answer is spot on. Also, I don't think it would be the best idea for the OP to try to learn the material ahead of time, but rather they should look it up as needed.
Jan
17
comment A question about opposite ring.
Every ring is the opposite of some other ring... They don't form a special class of rings. Any general result about "opposite rings" is a result about all rings. As for their utility, I think it is merely formal, for instance, if one doesn't want to talk about left and right modules, opposite rings come into play. Although there are important constructions involving the opposite of a ring, for instance, given a ring $R$, the ring structure on $R\otimes R^{\mathrm{op}}$ has some utility.
Jan
17
comment Showing that $|N \cap Z(G)| > 1$ for normal subgroups of p-groups
This is because, by definition of $i$, $Z_{i-1}\cap N=\lbrace e\rbrace$.
Jan
17
comment Prove $N\cap Z(P)\ne e$ given a $p$-group $P$ and a normal subgroup $N$.
I have added an answer to the linked question using the upper central series.
Jan
17
answered Showing that $|N \cap Z(G)| > 1$ for normal subgroups of p-groups
Jan
17
comment Prove $N\cap Z(P)\ne e$ given a $p$-group $P$ and a normal subgroup $N$.
Just a minor detail: you want the intersection to be larger than $e$ instead of non empty.
Jan
17
answered Does this theorem hold for Banach space?
Jan
17
comment Definition of CW complex
The $\kappa_i$ are even closed embeddings (by definition of when a subset is closed in $X$).
Jan
17
comment Definition of CW complex
Yes, $X$ is the colimit of the diagram $$X_0\hookrightarrow X_1\hookrightarrow X_2\hookrightarrow\cdots$$
Jan
16
reviewed Leave Open Metric $p := p(x,y)= \min(|x-y|, 1- |x-y|)$ $x,y \in [0,1)^2$. Prove metric space is compact.