mathlib
195fcd60 - refactor(topology/uniform_space/basic): review API (#18516)

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2 years ago
refactor(topology/uniform_space/basic): review API (#18516) ### API about uniform embeddings * Add `mk_iff` to `uniform_inducing` and `uniform_embedding`. * Move lemmas about `uniform_inducing` up. * Add `uniform_inducing.comap_uniform_space`, `uniform_inducing_iff'`, and `filter.has_basis.uniform_inducing_iff`. * Add `uniform_embedding_iff'`, `filter.has_basis.uniform_embedding_iff'`, and `filter.has_basis.uniform_embedding_iff`. * Drop `uniform_embedding_def` and `uniform_embedding_def'`. * Add `uniform_embedding_iff_uniform_inducing`. ### Other changes * Add `rescale_to_shell_semi_normed_zpow` and `rescale_to_shell_zpow`. * Generalize `continuous_linear_map.antilipschitz_of_uniform_embedding` to `continuous_linear_map.antilipschitz_of_embedding`, add an even more general version `linear_map.antilipschitz_of_comap_nhds_le`. * Use `fully_applied := ff` to generate `equiv.prod_congr_apply`. * Use `edist := λ _ _, 0` in `metric_space` instances for `empty` and `punit`. * Add `inducing.injective`, `inducing.embedding`, and `embedding_iff_inducing` * Allow `Sort*`s in `filter.has_basis.uniform_continuous_iff` and `filter.has_basis.uniform_continuous_on_iff`. * Rename * `metric.of_t0_pseudo_metric_space` to `metric_space.of_t0_pseudo_metric_space`; * `emetric.of_t0_pseudo_emetric_space` to `emetric_space.of_t0_pseudo_emetric_space`; * `metric.metric_space.to_emetric_space` to `metric_space.to_emetric_space`; * `uniform_embedding_iff'` to `emetric.uniform_embedding_iff'`
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