Theorems · Theorem · Lie groups
Continuous.mul
∀ {M : Type u_1} [inst : TopologicalSpace M] [inst_1 : Mul M] [ContinuousMul M] {X : Type u_2}
[inst_3 : TopologicalSpace X] {f g : X → M}, Continuous f → Continuous g → Continuous (f * g)- Defined in
- Mathlib.Topology.Algebra.Monoid.Defs
- Cited by
- 39 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Continuousstatement and proof · cited by 2,592
- ContinuousMulstatement and proof · cited by 343
- continuous_mulproof · cited by 41
- Continuous.comp₂proof · cited by 16
Cited by39
Results whose statement or proof uses this declaration.
- HasSum.mul_leftproof · cited by 25
- HasSum.mul_rightproof · cited by 11
- Continuous.fun_mulproof · cited by 4
- PhragmenLindelof.horizontal_stripproof · cited by 3
- Continuous.divproof · cited by 3
- Continuous.div₀proof · cited by 3
- Orientation.continuousAt_oangleproof · cited by 2
- continuous_algebraMap_iff_smulproof · cited by 2
- bernoulliFourierCoeff_recurrenceproof · cited by 2
- Polynomial.continuous_eval₂proof · cited by 2
- Real.continuous_mulExpNegMulSqproof · cited by 1
- DirichletCharacter.LFunction_changeLevelproof · cited by 1