Theorems · Theorem · Lie groups
ContinuousOn.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} {s : Set X}, ContinuousOn f s → ContinuousOn g s → ContinuousOn (f * g) s- Defined in
- Mathlib.Topology.Algebra.Monoid.Defs
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 73 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.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- ContinuousOnstatement and proof · cited by 1,411
- ContinuousMulstatement and proof · cited by 343
- ContinuousWithinAt.mulproof · cited by 4
Cited by17
Results whose statement or proof uses this declaration.
- ContinuousOn.fun_mulproof · cited by 11
- Real.GammaIntegral_convergentproof · cited by 5
- Complex.norm_log_sub_logTaylor_leproof · cited by 4
- Complex.GammaIntegral_convergentproof · cited by 3
- exists_ratio_hasDerivAt_eq_ratio_slopeproof · cited by 3
- intervalIntegral.integral_deriv_mul_eq_sub_of_hasDeriv_rightproof · cited by 2
- image_le_of_liminf_slope_right_le_deriv_boundaryproof · cited by 2
- Real.continuousOn_rpowIntegrand₀₁_uncurryproof · cited by 2
- mellin_hasDerivAt_of_isBigO_rpowproof · cited by 2
- continuousOn_taylorWithinEvalproof · cited by 1
- Complex.continuousOn_norm_circleTransformBoundingFunctionproof · cited by 1
- Real.Gamma_mul_add_mul_le_rpow_Gamma_mul_rpow_Gammaproof · cited by 1