KnowraHeine–Borel theoremLinked fromLinked fromThe 13 pages that link to Heine–Borel theorem, each with the reason it gives.All 13Broader topic 1Related 7Compared with 5Tychonoff's theoremCompared with: It handles finite-dimensional Euclidean compactness, unlike arbitrary topological products.Compact operatorCompared with: Unlike finite-dimensional spaces, infinite-dimensional normed spaces have noncompact closed bounded balls.Banach–Alaoglu theoremCompared with: Banach–Alaoglu gives compactness from boundedness in a weaker topology, even in infinite dimensions.Tube lemmaCompared with: It gives a metric-space criterion for compactness, whereas the tube lemma is purely topological.Vitali covering lemmaCompared with: Compactness produces finite subcovers, while the Vitali lemma targets disjoint selections.