Theorems · Theorem · Lie groups
mulLeft_continuous
∀ {R : Type u_1} [inst : TopologicalSpace R] [inst_1 : NonUnitalNonAssocRing R] [IsSemitopologicalRing R] (x : R),
Continuous ⇑(AddMonoidHom.mulLeft x)In a topological semiring, the left-multiplication AddMonoidHom is continuous.
- Defined in
- Mathlib.Topology.Algebra.Ring.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
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.
- DFunLike.coestatement · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- AddMonoidHomstatement · cited by 3,230
- Continuousstatement · cited by 2,592
- NonUnitalNonAssocRingstatement and proof · cited by 354
- continuous_idproof · cited by 192
- IsSemitopologicalRingstatement and proof · cited by 130
- Continuous.const_mulproof · cited by 27
- AddMonoidHom.mulLeftstatement · cited by 23
Cited by2
Results whose statement or proof uses this declaration.
- NormedRing.inverse_add_normproof · cited by 1
- NormedRing.inverse_add_nth_orderproof · cited by 1