> [!theorem] > > Let $(X, \topo)$ be a [[Sigma-Compact LCH Space|sigma-compact LCH space]], and $\mathcal U$ be an [[Open Cover|open cover]] of $X$. Then there exists locally finite refinements $\mathcal V = \seqi{V}$ and $\mathcal W = \seqi{W}$ such that $W_i \subset \subset V_i$ for each $i \in I$.