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display for open? #2

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2d9acc8
swapping machines
zstone1 Oct 6, 2022
f114567
proof of open map
zstone1 Oct 6, 2022
5591c98
hausdorff accessible
zstone1 Oct 6, 2022
5a9187b
weak products equivalent
zstone1 Oct 6, 2022
5bc1e3a
changelog
zstone1 Oct 6, 2022
98478a4
strengthen join_product_weak
zstone1 Oct 6, 2022
ac42713
cleaning up proofs
zstone1 Oct 10, 2022
70b9dc6
typos
affeldt-aist Oct 26, 2022
0e63902
display for open?
affeldt-aist Oct 26, 2022
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8 changes: 8 additions & 0 deletions CHANGELOG_UNRELEASED.md
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Expand Up @@ -98,6 +98,14 @@
+ lemma `fsumEFin`
- in `lebesgue_measure.v`:
+ definition `ErealGenInftyO.R` and lemma `ErealGenInftyO.measurableE`
- in `classical_sets.v`:
+ lemma `preimage_range`
- in `topology.v`
+ definition `separates_points_from_closed`, `join_product`
+ lemma `hausdorff_accessible`
+ lemmas `weak_sep_cvg`, `weak_sep_nbhsE`, `weak_sep_openE`,
`join_product_continuous`, `join_product_open`, `join_product_inj`,
`join_product_weak`

### Changed
- in `topology.v`
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3 changes: 3 additions & 0 deletions classical/classical_sets.v
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Expand Up @@ -1226,6 +1226,9 @@ Proof. by case=> [t ?]; exists (f t). Qed.
Lemma preimage_image f A : A `<=` f @^-1` (f @` A).
Proof. by move=> a Aa; exists a. Qed.

Lemma preimage_range {A B : Type} (f : A -> B) : f @^-1` (range f) = [set: A].
Proof. by rewrite eqEsubset; split=> x // _; exists x. Qed.

Lemma image_preimage_subset f Y : f @` (f @^-1` Y) `<=` Y.
Proof. by move=> _ [t /= Yft <-]. Qed.

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