[Merged by Bors] - refactor(UniformSpace): change the definition #10901
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We had duplicated API between topological spaces and uniform spaces. In this PR I mostly deduplicate it with some exceptions: - `SeparationQuotient.lift'` and `SeparationQuotient.map` are leftovers from the old version that are designed to work with uniform spaces; - probably, some theorems/instances still assume `UniformSpace` when `TopologicalSpace` would work.
This is an abbreviation for `Filter.lim` that deduces `Nonempty` from `Cauchy`. Use it to drop unneeded `Nonempty`/`Inhabited` assumptions.
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- replace `isOpen_uniformity` with `nhds_eq_comap_uniformity` as I suggested in #2028 - don't extend `UniformSpace.Core` so that we can drop `refl`, as it follows from `nhds_eq_comap_uniformity`; - drop `UniformSpace.mk'` - can't be a `match_pattern` anymore; - deprecate `UniformSpace.ofNhdsEqComap`.
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- replace `isOpen_uniformity` with `nhds_eq_comap_uniformity` as I suggested in #2028 - don't extend `UniformSpace.Core` so that we can drop `refl`, as it follows from `nhds_eq_comap_uniformity`; - drop `UniformSpace.mk'` - can't be a `match_pattern` anymore; - deprecate `UniformSpace.ofNhdsEqComap`.
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- replace `isOpen_uniformity` with `nhds_eq_comap_uniformity` as I suggested in #2028 - don't extend `UniformSpace.Core` so that we can drop `refl`, as it follows from `nhds_eq_comap_uniformity`; - drop `UniformSpace.mk'` - can't be a `match_pattern` anymore; - deprecate `UniformSpace.ofNhdsEqComap`.
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- replace `isOpen_uniformity` with `nhds_eq_comap_uniformity` as I suggested in #2028 - don't extend `UniformSpace.Core` so that we can drop `refl`, as it follows from `nhds_eq_comap_uniformity`; - drop `UniformSpace.mk'` - can't be a `match_pattern` anymore; - deprecate `UniformSpace.ofNhdsEqComap`.
utensil
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- replace `isOpen_uniformity` with `nhds_eq_comap_uniformity` as I suggested in #2028 - don't extend `UniformSpace.Core` so that we can drop `refl`, as it follows from `nhds_eq_comap_uniformity`; - drop `UniformSpace.mk'` - can't be a `match_pattern` anymore; - deprecate `UniformSpace.ofNhdsEqComap`.
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- replace `isOpen_uniformity` with `nhds_eq_comap_uniformity` as I suggested in #2028 - don't extend `UniformSpace.Core` so that we can drop `refl`, as it follows from `nhds_eq_comap_uniformity`; - drop `UniformSpace.mk'` - can't be a `match_pattern` anymore; - deprecate `UniformSpace.ofNhdsEqComap`.
atarnoam
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- replace `isOpen_uniformity` with `nhds_eq_comap_uniformity` as I suggested in #2028 - don't extend `UniformSpace.Core` so that we can drop `refl`, as it follows from `nhds_eq_comap_uniformity`; - drop `UniformSpace.mk'` - can't be a `match_pattern` anymore; - deprecate `UniformSpace.ofNhdsEqComap`.
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- replace `isOpen_uniformity` with `nhds_eq_comap_uniformity` as I suggested in #2028 - don't extend `UniformSpace.Core` so that we can drop `refl`, as it follows from `nhds_eq_comap_uniformity`; - drop `UniformSpace.mk'` - can't be a `match_pattern` anymore; - deprecate `UniformSpace.ofNhdsEqComap`.
callesonne
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- replace `isOpen_uniformity` with `nhds_eq_comap_uniformity` as I suggested in #2028 - don't extend `UniformSpace.Core` so that we can drop `refl`, as it follows from `nhds_eq_comap_uniformity`; - drop `UniformSpace.mk'` - can't be a `match_pattern` anymore; - deprecate `UniformSpace.ofNhdsEqComap`.
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isOpen_uniformitywithnhds_eq_comap_uniformityas I suggested in refactor: redefine
UniformSpace#2028UniformSpace.Coreso that we can droprefl,as it follows from
nhds_eq_comap_uniformity;UniformSpace.mk'- can't be amatch_patternanymore;UniformSpace.ofNhdsEqComap.separationRel#10644UniformOnFun#10873