Theorems · Theorem · general topology

IsDenseEmbedding.prodMap

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {δ : Type u_4} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β]
  [inst_2 : TopologicalSpace γ] [inst_3 : TopologicalSpace δ] {e₁ : α → β} {e₂ : γ → δ},
  IsDenseEmbedding e₁ → IsDenseEmbedding e₂ → IsDenseEmbedding fun p => (e₁ p.1, e₂ p.2)

The product of two dense embeddings is a dense embedding.

Defined in

Mathlib.Topology.DenseEmbedding

Cited by

0 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpaceTopologicalSpace