Theorems · Theorem · Lie groups
IsTopologicalSemiring.continuousNeg_of_mul
Deprecated since 2026-03-13Use IsSemitopologicalSemiring.continuousNeg_of_mul instead.
∀ {R : Type u_1} [inst : TopologicalSpace R] [inst_1 : NonAssocRing R] [SeparatelyContinuousMul R], ContinuousNeg RAlias of IsSemitopologicalSemiring.continuousNeg_of_mul.
If 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
- 0 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
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Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
- NonAssocRingstatement · cited by 483
- SeparatelyContinuousMulstatement · cited by 133
- ContinuousNegstatement · cited by 119
- IsSemitopologicalSemiring.continuousNeg_of_mulproof · cited by 3
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