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Definition df-topgen 12171
Description: Define a function that converts a basis to its corresponding topology. Equivalent to the definition of a topology generated by a basis in [Munkres] p. 78. (Contributed by NM, 16-Jul-2006.)
Assertion
Ref Expression
df-topgen  |-  topGen  =  ( x  e.  _V  |->  { y  |  y  C_  U. ( x  i^i  ~P y ) } )
Distinct variable group:    x, y

Detailed syntax breakdown of Definition df-topgen
StepHypRef Expression
1 ctg 12165 . 2  class  topGen
2 vx . . 3  setvar  x
3 cvv 2687 . . 3  class  _V
4 vy . . . . . 6  setvar  y
54cv 1331 . . . . 5  class  y
62cv 1331 . . . . . . 7  class  x
75cpw 3511 . . . . . . 7  class  ~P y
86, 7cin 3071 . . . . . 6  class  ( x  i^i  ~P y )
98cuni 3740 . . . . 5  class  U. (
x  i^i  ~P y
)
105, 9wss 3072 . . . 4  wff  y  C_  U. ( x  i^i  ~P y )
1110, 4cab 2126 . . 3  class  { y  |  y  C_  U. (
x  i^i  ~P y
) }
122, 3, 11cmpt 3993 . 2  class  ( x  e.  _V  |->  { y  |  y  C_  U. (
x  i^i  ~P y
) } )
131, 12wceq 1332 1  wff  topGen  =  ( x  e.  _V  |->  { y  |  y  C_  U. ( x  i^i  ~P y ) } )
Colors of variables: wff set class
This definition is referenced by:  tgval  12248  eltg4i  12254  eltg3  12256  tg1  12258  tg2  12259  tgclb  12264
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