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Theorems · Theorem · general topology

IsMinOn.closure

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] [inst_2 : Preorder Y]
  [OrderClosedTopology Y] {f : X → Y} {s : Set X} {a : X},
  IsMinOn f s a → ContinuousOn f (closure s) → IsMinOn f (closure s) a
Defined in
Mathlib.Topology.Order.ExtrClosure
Cited by
1 results in Mathlib
Foundations
Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpacePreorderOrderClosedTopology
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IsExtrOn.closure · cited by 0IsExtrOn.closureSet · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpacePreorder · cited by 7952PreorderContinuousOn · cited by 1411ContinuousOnclosure · cited by 1254closureOrderClosedTopology · cited by 445OrderClosedTopologyIsMinOn · cited by 96IsMinOnIsMaxOn.closure · cited by 3IsMaxOn.closureIsMinOn.dual · cited by 2IsMinOn.dualIsMinOn.closureCITED BYCITES

Cites9

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Cited by1

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