[Merged by Bors] - feat(topology/{continuous_function/bounded, metric_space/algebra}): new mixin classes #8580
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…ew mixin classes (#8580) This PR defines mixin classes `has_lipschitz_add` and `has_bounded_smul` which are designed to abstract algebraic properties of metric spaces shared by normed groups/fields/modules and by `ℝ≥0`. This permits the bounded continuous functions `α →ᵇ ℝ≥0` to be naturally a topological (ℝ≥0)-module, by a generalization of the proof previously written for normed groups/fields/modules. Frankly, these typeclasses are a bit ad hoc -- but it all seems to work!
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This PR defines mixin classes
has_lipschitz_addandhas_bounded_smulwhich are designed to abstract algebraic properties of metric spaces shared by normed groups/fields/modules and byℝ≥0.This permits the bounded continuous functions
α →ᵇ ℝ≥0to be naturally a topological (ℝ≥0)-module, by a generalization of the proof previously written for normed groups/fields/modules.Frankly, these typeclasses are a bit ad hoc -- but it all seems to work!