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Definition df-nei 12347
Description: Define a function on topologies whose value is a map from a subset to its neighborhoods. (Contributed by NM, 11-Feb-2007.)
Assertion
Ref Expression
df-nei  |-  nei  =  ( j  e.  Top  |->  ( x  e.  ~P U. j  |->  { y  e. 
~P U. j  |  E. g  e.  j  (
x  C_  g  /\  g  C_  y ) } ) )
Distinct variable group:    g, j, x, y

Detailed syntax breakdown of Definition df-nei
StepHypRef Expression
1 cnei 12346 . 2  class  nei
2 vj . . 3  setvar  j
3 ctop 12203 . . 3  class  Top
4 vx . . . 4  setvar  x
52cv 1331 . . . . . 6  class  j
65cuni 3744 . . . . 5  class  U. j
76cpw 3515 . . . 4  class  ~P U. j
84cv 1331 . . . . . . . 8  class  x
9 vg . . . . . . . . 9  setvar  g
109cv 1331 . . . . . . . 8  class  g
118, 10wss 3076 . . . . . . 7  wff  x  C_  g
12 vy . . . . . . . . 9  setvar  y
1312cv 1331 . . . . . . . 8  class  y
1410, 13wss 3076 . . . . . . 7  wff  g  C_  y
1511, 14wa 103 . . . . . 6  wff  ( x 
C_  g  /\  g  C_  y )
1615, 9, 5wrex 2418 . . . . 5  wff  E. g  e.  j  ( x  C_  g  /\  g  C_  y )
1716, 12, 7crab 2421 . . . 4  class  { y  e.  ~P U. j  |  E. g  e.  j  ( x  C_  g  /\  g  C_  y ) }
184, 7, 17cmpt 3997 . . 3  class  ( x  e.  ~P U. j  |->  { y  e.  ~P U. j  |  E. g  e.  j  ( x  C_  g  /\  g  C_  y ) } )
192, 3, 18cmpt 3997 . 2  class  ( j  e.  Top  |->  ( x  e.  ~P U. j  |->  { y  e.  ~P U. j  |  E. g  e.  j  ( x  C_  g  /\  g  C_  y ) } ) )
201, 19wceq 1332 1  wff  nei  =  ( j  e.  Top  |->  ( x  e.  ~P U. j  |->  { y  e. 
~P U. j  |  E. g  e.  j  (
x  C_  g  /\  g  C_  y ) } ) )
Colors of variables: wff set class
This definition is referenced by:  neifval  12348
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