Theorems · Theorem · general topology

IsOpen.continuous_piecewise_of_specializes

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {s : Set X} {f g : X → Y}
  [inst_2 : DecidablePred fun x => x ∈ s],
  IsOpen s → Continuous f → Continuous g → (∀ (x : X), f x ⤳ g x) → Continuous (s.piecewise f g)

Defined in

Mathlib.Topology.Inseparable

Cited by

1 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceDecidablePred