Theorems · Theorem · general topology

connectedComponent_prod

∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] (x : α) (y : β),
  connectedComponent (x, y) = connectedComponent x ×ˢ connectedComponent y

The connected component of (x, y) in the product space is the product of the connected components of x and y.

Defined in

Mathlib.Topology.Connected.Basic

Cited by

0 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace