Mathlib Map

Theorems · Theorem · general topology

Continuous.if_const

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f g : α → β} (p : Prop)
  [inst_2 : Decidable p], Continuous f → Continuous g → Continuous fun a => if p then f a else g a
Defined in
Mathlib.Topology.Piecewise
Cited by
2 results in Mathlib
Foundations
Depth 8 from the axioms · uses Quot.sound
Assumes
TopologicalSpaceTopologicalSpaceDecidable
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Continuous.matrix_diagonal · cited by 3Continuous.matrix_diagonalContinuous.matrix_blockDiagonal · cited by 3Continuous.matrix_blockDi…TopologicalSpace · cited by 24529TopologicalSpaceContinuous · cited by 2592Continuouscontinuous_if_const · cited by 1continuous_if_constContinuous.if_constCITED BYCITES

Cites3

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

Cited by2

Results whose statement or proof uses this declaration.