diff --git a/CHANGELOG_UNRELEASED.md b/CHANGELOG_UNRELEASED.md index 8924b1821..542e55de0 100644 --- a/CHANGELOG_UNRELEASED.md +++ b/CHANGELOG_UNRELEASED.md @@ -168,7 +168,29 @@ - moved from `topology.v` to `boolp.v`: + lemmas `bigmax_geP`, `bigmax_gtP`, `bigmin_leP`, `bigmin_ltP` +- moved from `topology.v` to `separation_axioms.v`: `set_nbhs`, `set_nbhsP`, + `accessible_space`, `kolmogorov_space`, `hausdorff_space`, + `compact_closed`, `discrete_hausdorff`, `compact_cluster_set1`, + `compact_precompact`, `open_hausdorff`, `hausdorff_accessible`, + `accessible_closed_set1`, `accessible_kolmogorov`, + `accessible_finite_set_closed`, `subspace_hausdorff`, `order_hausdorff`, + `ball_hausdorff`, `Rhausdorff`, `close`, `closeEnbhs`, `closeEonbhs`, + `close_sym`, `cvg_close`, `close_refl`, `cvgx_close`, `cvgi_close`, + `cvg_toi_locally_close`, `closeE`, `close_eq`, `cvg_unique`, `cvg_eq`, + `cvgi_unique`, `close_cvg`, `lim_id`, `lim_near_cst`, `lim_cst`, + `entourage_close`, `close_trans`, `close_cvgxx`, `cvg_closeP`, + `ball_close`, `normal_space`, `regular_space`, `compact_regular`, + `uniform_regular`, `totally_disconnected`, `zero_dimensional`, + `discrete_zero_dimension`, `zero_dimension_totally_disconnected`, + `zero_dimensional_ray`, `type`, `countable_uniform_bounded`, + `countable_uniform`, `sup_pseudometric`, `countable_uniformityT`, `gauge`, + `iter_split_ent`, `gauge_ent`, `gauge_filter`, `gauge_refl`, `gauge_inv`, + `gauge_split`, `gauge_countable_uniformity`, `uniform_pseudometric_sup`, + `perfect_set`, `perfectTP`, and `perfect_set2`. ### Renamed +- in file `topology.v` -> `separation_axioms.v` + + `totally_disconnected_cvg` -> `zero_dimensional_cvg`. + ### Generalized diff --git a/theories/separation_axioms.v b/theories/separation_axioms.v index 847b22641..bc3fe9f1c 100644 --- a/theories/separation_axioms.v +++ b/theories/separation_axioms.v @@ -118,7 +118,6 @@ Proof. by move=> p q /(_ _ _ (discrete_set1 p) (discrete_set1 q)) [] // x [] -> ->. Qed. - Lemma compact_cluster_set1 (x : T) F V : hausdorff_space -> compact V -> nbhs x V -> ProperFilter F -> F V -> cluster F = [set x] -> F --> x. @@ -234,7 +233,6 @@ move=> npzq; exists (`]-oo, q[, `]p, +oo[)%classic; split => //=. by apply: npzq; exists r; rewrite rz zr. Qed. - Section ball_hausdorff. Variables (R : numDomainType) (T : pseudoMetricType R). @@ -329,8 +327,6 @@ Proof. by rewrite -closeE //; apply: cvg_close. Qed. Lemma cvgi_unique {U : Type} {F} {FF : ProperFilter F} (f : U -> set T) : {near F, is_fun f} -> is_subset1 [set x : T | f `@ F --> x]. Proof. by move=> ffun fx fy; rewrite -closeE //; exact: cvgi_close. Qed. - - End separated_topologicalType. Section separated_ptopologicalType. @@ -370,7 +366,6 @@ Lemma cvgi_lim {U} {F} {FF : ProperFilter F} (f : U -> T -> Prop) (l : T) : Proof. move=> f_prop fl; apply: get_unique => // l' fl'; exact: cvgi_unique _ fl' fl. Qed. - End separated_ptopologicalType. #[deprecated(since="mathcomp-analysis 0.6.0", note="renamed to `cvg_lim`")] @@ -411,7 +406,6 @@ apply/xsectionP; apply: (entourage_split x) => //. by have := cxy _ (entourage_inv (entourage_split_ent entA)). Qed. - Lemma cvg_closeP { U : puniformType} (F : set_system U) (l : U) : ProperFilter F -> F --> l <-> ([cvg F in U] /\ close (lim F) l). Proof. @@ -488,8 +482,6 @@ Local Close Scope relation_scope. #[global] Hint Resolve uniform_regular : core. - - Section totally_disconnected. Implicit Types T : topologicalType. @@ -574,6 +566,7 @@ exists V; split; first split. Qed. End totally_disconnected. + (* This section proves that uniform spaces, with a countable base for their entourage, are metrizable. The definition of this metric is rather arcane, and the proof is tough. That's ok because the resulting metric is not @@ -901,7 +894,6 @@ Qed. End countable_uniform. - Module Exports. HB.reexport. End Exports. End countable_uniform. Export countable_uniform.Exports. @@ -929,7 +921,6 @@ HB.instance Definition _ : PseudoMetric R S := End sup_pseudometric. - Module gauge. Section gauge. Local Open Scope relation_scope. @@ -1057,4 +1048,4 @@ move=> Unxy x Ox; have [] := Unxy _ Ox; first by exists x. by move=> y [] ? [->] -> /eqP. Qed. -End perfect_sets. \ No newline at end of file +End perfect_sets.