--- a/src/Topology.agda	Thu Dec 29 10:58:42 2022 +0900
+++ b/src/Topology.agda	Thu Dec 29 14:42:28 2022 +0900
@@ -65,13 +65,6 @@
    g∩ : {x y : HOD} → genTop P x → genTop P y → genTop P (x ∩ y)
    g∪ : {Q x : HOD} → Q ⊆ P → genTop P (Union Q)
 
--- Limit point
-
-record LP { L : HOD}  (top : Topology L) ( S x : HOD ) (S⊆PL :  S ⊆ Power L ) ( S∋x : S ∋ x ) : Set (suc n) where
-   field
-      neip   : {y : HOD} → OS top ∋ y → y ∋ x → HOD
-      isNeip : {y : HOD} → (o∋y : OS top ∋ y ) → (y∋x : y ∋ x ) → ¬ ( x ≡ neip o∋y y∋x) ∧ ( y ∋ neip o∋y y∋x )
-       
 -- Finite Intersection Property
 
 data Finite-∩ (S : HOD) : HOD → Set (suc n) where
@@ -166,9 +159,35 @@
 
 Tychonoff : {P Q : HOD } → (TP : Topology P) → (TQ : Topology Q)  → Compact TP → Compact TQ   → Compact (TP Top⊗ TQ)
 Tychonoff {P} {Q} TP TQ CP CQ = FIP→Compact (TP Top⊗ TQ) (UFLP→FIP (TP Top⊗ TQ) uflp ) where
-    uflp : {L : HOD} (LP : L ⊆ Power (ZFP P Q)) (F : Filter LP)
-            (uf : ultra-filter {L} {_} {LP} F) → UFLP (TP Top⊗ TQ) LP F uf
-    uflp {L} LP F uf = record { limit = ? ; P∋limit = ? ; is-limit = ? }
+    uflp : {L : HOD} (LPQ : L ⊆ Power (ZFP P Q)) (F : Filter LPQ)
+            (uf : ultra-filter {L} {_} {LPQ} F) → UFLP (TP Top⊗ TQ) LPQ F uf
+    uflp {L} LPQ F uf = record { limit = ? ; P∋limit = ? ; is-limit = ? } where
+         lprod : {x y : Ordinal } → (ly : odef L y) → odef (ZFP P Q) x
+         lprod {x} {y} ly = LPQ ly x ?
+         -- LP : HOD  
+         -- LP = Replace' L ( λ x lx → Replace' x ( λ z xz → * ( zπ1 (LPQ lx (& z) (subst (λ k → odef k (& z)) (sym *iso) xz )))) )
+         LP : HOD  
+         LP = record { od = record { def = λ x → {y z : Ordinal } → (ly : odef L y) → x ≡ & ( L→P ly ) }
+          ; odmax = & P ; <odmax = ? }   where
+            L→P : {y : Ordinal } → odef L y → HOD
+            L→P {y} ly = record { od = record { def = λ x → {z : Ordinal } → (yz : odef (* y) z) → zπ1 (LPQ ly z yz )  ≡ x } 
+               ; odmax = & P ; <odmax = ? }
+         LPP : LP ⊆ Power P
+         LPP = ?
+         FP : Filter LPP
+         FP = record { filter = ? ; f⊆L = ? ; filter1 = ? ; filter2 = ? }
+         uFP : ultra-filter FP
+         uFP = record { proper = ? ; ultra = ? }
+         LQ : HOD  
+         LQ = record { od = record { def = λ x → {y z : Ordinal } → (ly : odef L y) → x ≡ & ( L→Q ly ) }
+          ; odmax = & P ; <odmax = ? }   where
+            L→Q : {y : Ordinal } → odef L y → HOD
+            L→Q {y} ly = record { od = record { def = λ x → {z : Ordinal } → (yz : odef (* y) z) → zπ2 (LPQ ly z yz )  ≡ x } 
+               ; odmax = & Q ; <odmax = ? }
+         LQQ : LQ ⊆ Power Q
+         LQQ = ?
+         uflpp : UFLP {P} TP {LP} LPP FP uFP
+         uflpp = ?