KnowraTychonoff's theoremLinked fromLinked fromThe 10 pages that link to Tychonoff's theorem, each with the reason it gives.All 10Related 10Axiom of choiceRelated: Choice principles underlie the general product compactness result used throughout topology.Compact spaceRelated: It makes compactness available in products with arbitrarily many factors.Zorn's lemmaRelated: Its general proof uses the ultrafilter characterization of compactness and the ultrafilter lemma.Choice functionRelated: Its general form is equivalent to the axiom of choice.Product topologyRelated: Its compactness conclusion depends on using the product rather than the box topology.Banach–Alaoglu theoremRelated: It supplies compactness for the product space containing the dual unit ball.General topologyRelated: It shows how compactness behaves under a fundamental construction of spaces.Tube lemmaRelated: Tube-lemma arguments appear in proofs connecting compact factors and compact product spaces.De Bruijn–Erdős theorem (graph theory)Related: It supplies compactness for all vertex color assignments at once.Teichmüller–Tukey lemmaRelated: Its general form is equivalent to the axiom of choice, linking it to the lemma’s strength.