11:34 PM
@ACuriousMind So I have $\Omega\subset\Bbb R^2$ open, $z,w\in\Omega$
I want a curve $\gamma$ from $z$ to $w$ such that some neighborhood $U$ of $\gamma$ is contained in $\Omega$ and is simply connected
I know how to do this, just take an embedded curve and then do a tubular neighborhood
But I probably can't use that construction
is there a more elementary construction?
Covering by balls works but it's hard to justify correctly