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fixes #1468, fixes #1467 #1469

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Merged
affeldt-aist merged 1 commit into from
Feb 12, 2025
Merged

fixes #1468, fixes #1467 #1469

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3 changes: 3 additions & 0 deletions CHANGELOG_UNRELEASED.md
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Expand Up @@ -153,6 +153,9 @@
- in `Rstruct.v`:
+ lemma `RsqrtE`

- in `normedtype.v`:
+ `cvg_at_right_filter`, `cvg_at_left_filter`

### Deprecated

### Removed
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8 changes: 5 additions & 3 deletions theories/normedtype.v
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Expand Up @@ -1514,10 +1514,12 @@ End open_itv_subset.
Section at_left_right_topologicalType.
Variables (R : numFieldType) (V : topologicalType) (f : R -> V) (x : R).

Lemma cvg_at_right_filter : f z @[z --> x] --> f x -> f z @[z --> x^'+] --> f x.
Lemma cvg_at_right_filter (l : V) :
f z @[z --> x] --> l -> f z @[z --> x^'+] --> l.
Proof. exact: (@cvg_within_filter _ _ _ (nbhs x)). Qed.

Lemma cvg_at_left_filter : f z @[z --> x] --> f x -> f z @[z --> x^'-] --> f x.
Lemma cvg_at_left_filter (l : V) :
f z @[z --> x] --> l -> f z @[z --> x^'-] --> l.
Proof. exact: (@cvg_within_filter _ _ _ (nbhs x)). Qed.

Lemma cvg_at_right_within : f x @[x --> x^'+] --> f x ->
Expand Down Expand Up @@ -2494,7 +2496,7 @@ End prod_NormedModule.
Section example_of_sharing.
Variables (K : numDomainType).

Example matrix_triangke m n (M N : 'M[K]_(m.+1, n.+1)) :
Example matrix_triangle m n (M N : 'M[K]_(m.+1, n.+1)) :
`|M + N| <= `|M| + `|N|.
Proof. exact: ler_normD. Qed.

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1 change: 0 additions & 1 deletion theories/topology_theory/topology_structure.v
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Expand Up @@ -919,7 +919,6 @@ Proof. by rewrite -interiorC interiorEbigcup. Qed.
#[deprecated(since="mathcomp-analysis 1.7.0", note="use `interiorC` and `interiorEbigcup` instead")]
Notation closureC := closureC_deprecated (only parsing).


Definition dense (T : topologicalType) (S : set T) :=
forall (O : set T), O !=set0 -> open O -> O `&` S !=set0.

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