Good reference for partitions of unity?

Question

I am reading about Sobolev Spaces and regularity theory of PDEs. The partition of unity lemma, as stated in Haim Brezis' Functional Analysis, Sobolev Spaces and Partial Differential Equations, is as follows:

Given $C \in \mathbb{R}^n$ a compact set and $U_0,U_1,...,U_k$ an open covering $C$ (i.e $C \subset \bigcup_{i=0}^{k}U_i$), there exist $k+1$ functions $\theta_0,...,\theta_k \in C^{\infty}(\mathbb{R}^n)$ such that:

1. $0 \leq \theta_i(x) \leq 1 \quad \forall i=0,1,...,k$.
   2. $\sum_{i=0}^k\theta_i(x)=1 $.
   3. $sop(\theta_i) \subset U_i \quad \forall i =1,2,...,k$.
   4. $sop(\theta_0) \subset \mathbb{R}^n-C$.

If $C$ is the boundary of an open set $\Omega$, then $\theta_{0 |\Omega} \in C_c^{\infty}(\Omega)$.

Could you please provide me some good reference in which I can read the proof of this result?