KnowraWeak topologyLinked fromLinked fromThe 12 pages that link to Weak topology, each with the reason it gives.All 12Broader topic 1Related 9Narrower topic 1Compared with 1Open setCompared with: It shows how requiring fewer open sets can preserve selected continuity properties.Dual spaceRelated: The dual space determines the weak topology on a vector space through its evaluations.Functional analysisRelated: Weak convergence can hold when norm convergence fails, aiding compactness arguments.Hausdorff spaceRelated: Weak topologies on Hausdorff locally convex spaces remain Hausdorff when the defining functionals separate points.Weak convergenceRelated: It turns convergence under all chosen tests into ordinary topological convergence.Hahn–Banach theoremRelated: The theorem ensures enough functionals to distinguish points and define this topology.Product topologyRelated: It shares the initial-topology construction, but its generating maps need not be coordinate projections.Prokhorov's theoremNarrower topic: The theorem belongs to the development of weak topologies on spaces of measures.Continuous mapping theoremRelated: It gives the topological framework in which convergence in distribution is expressed.Eberlein–Šmulian theoremBroader topic: Compactness in this topology is the theorem’s topological condition.Bipolar theoremRelated: The closure in the conclusion depends on the topology selected by the dual pairing.Ryll-Nardzewski fixed-point theoremRelated: Compactness in weak topologies often makes fixed-point hypotheses applicable in analysis.