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Definition df-topspOLD 16653
Description: Define the class of all topological spaces, each of which is an ordered pair the second of which is a topology on the first. See istps5OLD 16678 for a standard way to express a topological space. (Contributed by NM, 8-Mar-2006.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
df-topspOLD  |-  TopSp OLD  =  { <. x ,  y
>.  |  ( y  e.  Top  /\  x  = 
U. y ) }
Distinct variable group:    x, y

Detailed syntax breakdown of Definition df-topspOLD
StepHypRef Expression
1 ctpsOLD 16649 . 2  class  TopSp OLD
2 vy . . . . . 6  set  y
32cv 1631 . . . . 5  class  y
4 ctop 16647 . . . . 5  class  Top
53, 4wcel 1696 . . . 4  wff  y  e. 
Top
6 vx . . . . . 6  set  x
76cv 1631 . . . . 5  class  x
83cuni 3843 . . . . 5  class  U. y
97, 8wceq 1632 . . . 4  wff  x  = 
U. y
105, 9wa 358 . . 3  wff  ( y  e.  Top  /\  x  =  U. y )
1110, 6, 2copab 4092 . 2  class  { <. x ,  y >.  |  ( y  e.  Top  /\  x  =  U. y
) }
121, 11wceq 1632 1  wff  TopSp OLD  =  { <. x ,  y
>.  |  ( y  e.  Top  /\  x  = 
U. y ) }
Colors of variables: wff set class
This definition is referenced by:  eltopspOLD  16672  tpsexOLD  16673  istpsOLD  16674
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