Theorems · Theorem · general topology
IsLocalMax.comp_antitone
∀ {α : Type u} {β : Type v} {γ : Type w} [inst : TopologicalSpace α] [inst_1 : Preorder β] [inst_2 : Preorder γ]
{f : α → β} {a : α}, IsLocalMax f a → ∀ {g : β → γ}, Antitone g → IsLocalMin (g ∘ f) a- Defined in
- Mathlib.Topology.Order.LocalExtr
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Quot.sound
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Preorderstatement and proof · cited by 7,952
- Antitonestatement and proof · cited by 563
- IsLocalMaxstatement and proof · cited by 50
- IsLocalMinstatement · cited by 45
- IsMaxFilter.comp_antitoneproof · cited by 4
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