Math When Heine-Borel theorem applies By admin October 24, 2016 October 24, 2016 Question: What condition of the Heine-Borel Theorem does this not meet? Consider Q\mathbb Q with metric d(p,q)=|p−q|d(p,q) = |p-q|, and E={q:2 Let f:R→Rf : \mathbb{R} \rightarrow \mathbb{R} be continuous. Show that f(R)=Rf(\mathbb{R}) = \mathbb{R} Normal Subgroups and Lagrange’s Theorem