Hello everyone I am looking for a couple of references:
Claim 1 states that an open and connected set in $R^n$ is path-connected. Or more general an open, connected and locally connected set is path-connected.
Claim 2 states that $L^p_{BC}$ is a subset of $L^1_{BC}$, where $L^p_{BC}$ is the set of continuous and bounded functions such that $\int_{\mathbb{R}} |f(x)| dx < \infty$
Thanks in advance for any help.