2
votes
1answer
97 views

Lipschitz manifold and semi-algebraic is Lipschitz graph?

It is known that there are Lipschitz manifolds that are not Lipschitz graphs and $C^1$ manifold is locally $C^1$ graph. If $M\subset \mathbb{R}^m$ is a Lipschitz manifold (with the outer distance) ...
0
votes
1answer
106 views

Supremum and Infinmum of function with singularity

My original approach was to let $f = \sin (1/x)$ and do regular calculus. However, I found that it wasn't so simple. I graphed the function on Mathematica and it was even worse! It seems like the ...