Mercurial > hg > Members > kono > Proof > ZF-in-agda
diff src/Topology.agda @ 1228:e3f20bc4fac9
last part of Tychonoff
author | Shinji KONO <kono@ie.u-ryukyu.ac.jp> |
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date | Wed, 08 Mar 2023 10:28:55 +0900 |
parents | 362e43a1477c |
children | 45cd80181a29 |
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--- a/src/Topology.agda Tue Mar 07 19:19:03 2023 +0900 +++ b/src/Topology.agda Wed Mar 08 10:28:55 2023 +0900 @@ -224,12 +224,14 @@ -- Product Topology is not -- ZFP (OS TP) (OS TQ) (box) +-- Rectangle subset (zπ1 ⁻¹ p) record BaseP {P : HOD} (TP : Topology P ) (Q : HOD) (x : Ordinal) : Set n where field p : Ordinal op : odef (OS TP) p prod : x ≡ & (ZFP (* p) Q ) +-- Rectangle subset (zπ12⁻¹ q ) record BaseQ (P : HOD) {Q : HOD} (TQ : Topology Q ) (x : Ordinal) : Set n where field q : Ordinal @@ -287,7 +289,7 @@ data Finite-∪ (S : HOD) : Ordinal → Set n where fin-e : Finite-∪ S o∅ - fin-i : {x : Ordinal } → odef S x → Finite-∪ S (& ( * x , * x )) + fin-i : {x : Ordinal } → odef S x → Finite-∪ S (& ( * x , * x )) -- an element of S fin-∪ : {x y : Ordinal } → Finite-∪ S x → Finite-∪ S y → Finite-∪ S (& (* x ∪ * y)) -- Finite-∪ S y → Union y ⊆ S @@ -621,8 +623,9 @@ open Filter --- Ultra Filter has limit point - +-- +-- {v | Neighbor lim v} set of u ⊆ v ⊆ P where u is an open set u ∋ x +-- record Neighbor {P : HOD} (TP : Topology P) (x v : Ordinal) : Set n where field u : Ordinal