Theorems · Theorem · geometry

ContinuousAffineMap.contLinear_eq_zero_iff_exists_const

∀ {R : Type u_1} {V : Type u_2} {W : Type u_3} {P : Type u_4} {Q : Type u_5} [inst : Ring R] [inst_1 : AddCommGroup V]
  [inst_2 : Module R V] [inst_3 : TopologicalSpace P] [inst_4 : AddTorsor V P] [inst_5 : AddCommGroup W]
  [inst_6 : Module R W] [inst_7 : TopologicalSpace Q] [inst_8 : AddTorsor W Q] [inst_9 : TopologicalSpace V]
  [inst_10 : IsTopologicalAddTorsor P] [inst_11 : TopologicalSpace W] [inst_12 : IsTopologicalAddTorsor Q]
  (f : P →ᴬ[R] Q), f.contLinear = 0 ↔ ∃ q, f = ContinuousAffineMap.const R P q

Defined in

Mathlib.Topology.Algebra.ContinuousAffineMap

Cited by

0 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleTopologicalSpaceAddTorsorAddCommGroupModuleTopologicalSpaceAddTorsorTopologicalSpaceIsTopologicalAddTorsorTopologicalSpaceIsTopologicalAddTorsor