Theorems · Theorem · Lie groups
IsSemitopologicalSemiring.continuousNeg_of_mul
∀ {R : Type u_1} [inst : TopologicalSpace R] [inst_1 : NonAssocRing R] [SeparatelyContinuousMul R], ContinuousNeg RIf R is a ring with a separately continuous multiplication, then negation is continuous as
well since it is just multiplication with -1.
- Defined in
- Mathlib.Topology.Algebra.Ring.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- one_mulproof · cited by 2,841
- Continuousproof · cited by 2,592
- neg_mulproof · cited by 654
- NonAssocRingstatement and proof · cited by 483
- continuous_idproof · cited by 192
- SeparatelyContinuousMulstatement and proof · cited by 133
- ContinuousNegstatement · cited by 119
- Continuous.const_mulproof · cited by 27
Cited by3
Results whose statement or proof uses this declaration.
- IsTopologicalSemiring.continuousNeg_of_mulproof · cited by 0
- IsSemitopologicalSemiring.toIsSemitopologicalRingproof · cited by 0
- IsTopologicalSemiring.toIsTopologicalRingproof · cited by 0