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uniform nonsense
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import analysis.topology.uniform_space | |
universes u v | |
variables (α : Type u) [uniform_space α] | |
structure completion_package := | |
(space : Type u) | |
(uniform_structure : uniform_space space) | |
(completeness : complete_space space) | |
(separation : separated space) | |
(map : α → space) | |
(uniform_continuity : uniform_continuous map) | |
(lift : ∀ {β : Type u} (f : α → β), space → β) | |
(lift_uc : ∀ {β : Type u} [uniform_space β] [complete_space β] [separated β] {f : α → β}, | |
uniform_continuous f → uniform_continuous (lift f)) | |
(lift_lifts : ∀ {β : Type u} [uniform_space β] [complete_space β] [separated β] {f : α → β}, | |
uniform_continuous f → f = (lift f) ∘ map) | |
(lift_unique : ∀ {β : Type u} [uniform_space β] [complete_space β] [separated β] | |
{f : α → β} (h : uniform_continuous f) {g : space → β}, | |
uniform_continuous g → f = g ∘ map → g = lift f) | |
variables (pkg pkg' : completion_package α) {α} | |
def compare (pkg pkg' : completion_package α) : pkg.space → pkg'.space := | |
pkg.lift pkg'.map | |
lemma uniform_continuous_compare : | |
@uniform_continuous _ _ pkg.uniform_structure pkg'.uniform_structure (compare pkg pkg') := | |
begin | |
haveI := pkg'.uniform_structure, | |
exact pkg.lift_uc pkg'.uniform_continuity, | |
sorry | |
end | |
open function | |
lemma compare_iso_aux : left_inverse (compare pkg pkg') (compare pkg' pkg) := | |
sorry |
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