Theorems · Theorem · general topology

AffineMap.lineMap_continuous

∀ {R : Type u_1} {V : Type u_2} {P : Type u_3} [inst : AddCommGroup V] [inst_1 : TopologicalSpace V]
  [inst_2 : AddTorsor V P] [inst_3 : TopologicalSpace P] [IsTopologicalAddTorsor P] [inst_5 : Ring R]
  [inst_6 : Module R V] [inst_7 : TopologicalSpace R] [ContinuousSMul R V] {p q : P},
  Continuous ⇑(AffineMap.lineMap p q)

The line map is continuous.

Defined in

Mathlib.Topology.Algebra.Affine

Cited by

7 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupTopologicalSpaceAddTorsorTopologicalSpaceIsTopologicalAddTorsorRingModuleTopologicalSpaceContinuousSMul