Theorems · Theorem · general topology

Continuous.piecewise

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f g : α → β} {s : Set α}
  [inst_2 : (a : α) → Decidable (a ∈ s)],
  (∀ a ∈ frontier s, f a = g a) → Continuous f → Continuous g → Continuous (s.piecewise f g)

Defined in

Mathlib.Topology.Piecewise

Cited by

2 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceDecidable