Theorems · Theorem · general topology

DenseRange.equalizer

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : TopologicalSpace β] [inst_1 : TopologicalSpace γ] [T2Space γ]
  {f : α → β}, DenseRange f → ∀ {g h : β → γ}, Continuous g → Continuous h → g ∘ f = h ∘ f → g = h

Two continuous functions to a t2-space that agree on the dense range of a function are equal.

Defined in

Mathlib.Topology.DenseEmbedding

Cited by

7 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceT2Space