MathOverflow

For odd natural $n$ define the Euler quotient $E(n)=\frac{2^{\varphi(n)}-1 \bmod n^2}{n}$. If $n$ is prime then $E(n)$ is called Fermat quotient.$n$ is Wieferich number iff $E(n)=0$. There are only two Wiferich primes knownand it is an open problem if...

Im looking for examples of groups $G$ satisfying the following hypothesis:
$G$ acts cocompactly and admissibly on a contractible $CW$-complex $X$
The cell stabilizers are of type $FP_\infty$

Suppose we have a 1-Lipschitz function $f$ such that 1-Lipschitzness is preserved, with $D_A(f(X), f(Y)) \leq D_B(X, Y)$ for some metric spaces $A$ and $B$.
Does this also imply that $I(f(X); f(Y)) = I(X;Y)$? It seems intuitive that this would be the case if the 1-lipschitz function is injective, but I don't know if this is true, so that the mutual information is preserved under such invertible transformation...

It can be difficult to learn mathematics on your own from textbooks, and I often wish universities videotaped their mathematics courses and distributed them for free online. Fortunately, some universities do that (albeit to a very limited extent), and...