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Definition df-lp 16863
Description: Define a function on topologies whose value is the set of limit points of the subsets of the base set. See lpval 16866. (Contributed by NM, 10-Feb-2007.)
Assertion
Ref Expression
df-lp  |-  limPt  =  ( j  e.  Top  |->  ( x  e.  ~P U. j  |->  { y  |  y  e.  ( ( cls `  j ) `
 ( x  \  { y } ) ) } ) )
Distinct variable group:    x, j, y

Detailed syntax breakdown of Definition df-lp
StepHypRef Expression
1 clp 16861 . 2  class  limPt
2 vj . . 3  set  j
3 ctop 16626 . . 3  class  Top
4 vx . . . 4  set  x
52cv 1623 . . . . . 6  class  j
65cuni 3829 . . . . 5  class  U. j
76cpw 3627 . . . 4  class  ~P U. j
8 vy . . . . . . 7  set  y
98cv 1623 . . . . . 6  class  y
104cv 1623 . . . . . . . 8  class  x
119csn 3642 . . . . . . . 8  class  { y }
1210, 11cdif 3151 . . . . . . 7  class  ( x 
\  { y } )
13 ccl 16750 . . . . . . . 8  class  cls
145, 13cfv 5222 . . . . . . 7  class  ( cls `  j )
1512, 14cfv 5222 . . . . . 6  class  ( ( cls `  j ) `
 ( x  \  { y } ) )
169, 15wcel 1685 . . . . 5  wff  y  e.  ( ( cls `  j
) `  ( x  \  { y } ) )
1716, 8cab 2271 . . . 4  class  { y  |  y  e.  ( ( cls `  j
) `  ( x  \  { y } ) ) }
184, 7, 17cmpt 4079 . . 3  class  ( x  e.  ~P U. j  |->  { y  |  y  e.  ( ( cls `  j ) `  (
x  \  { y } ) ) } )
192, 3, 18cmpt 4079 . 2  class  ( j  e.  Top  |->  ( x  e.  ~P U. j  |->  { y  |  y  e.  ( ( cls `  j ) `  (
x  \  { y } ) ) } ) )
201, 19wceq 1624 1  wff  limPt  =  ( j  e.  Top  |->  ( x  e.  ~P U. j  |->  { y  |  y  e.  ( ( cls `  j ) `
 ( x  \  { y } ) ) } ) )
Colors of variables: wff set class
This definition is referenced by:  lpfval  16865
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