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Theorems · Theorem · dynamical systems

Continuous.flow

∀ {τ : Type u_1} {α : Type u_2} [inst : TopologicalSpace τ] [inst_1 : TopologicalSpace α] [inst_2 : AddZero τ]
  (ϕ : Flow τ α) {β : Type u_3} [inst_3 : TopologicalSpace β] {t : β → τ},
  Continuous t → ∀ {f : β → α}, Continuous f → Continuous fun x => ϕ.toFun (t x) (f x)

Alias of Flow.continuous.

Defined in
Mathlib.Dynamics.Flow
Cited by
1 results in Mathlib
Foundations
Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpaceAddZeroTopologicalSpace
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Around this declaration

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

Flow.isInvariant_omegaLimit · cited by 1Flow.isInvariant_omegaLim…TopologicalSpace · cited by 24529TopologicalSpaceContinuous · cited by 2592ContinuousAddZero · cited by 87AddZeroFlow · cited by 46FlowFlow.toFun · cited by 34Flow.toFunFlow.continuous · cited by 2Flow.continuousContinuous.flowCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.