MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-lp Structured version   Unicode version

Definition df-lp 19807
Description: Define a function on topologies whose value is the set of limit points of the subsets of the base set. See lpval 19810. (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 19805 . 2  class  limPt
2 vj . . 3  setvar  j
3 ctop 19564 . . 3  class  Top
4 vx . . . 4  setvar  x
52cv 1397 . . . . . 6  class  j
65cuni 4235 . . . . 5  class  U. j
76cpw 3999 . . . 4  class  ~P U. j
8 vy . . . . . . 7  setvar  y
98cv 1397 . . . . . 6  class  y
104cv 1397 . . . . . . . 8  class  x
119csn 4016 . . . . . . . 8  class  { y }
1210, 11cdif 3458 . . . . . . 7  class  ( x 
\  { y } )
13 ccl 19689 . . . . . . . 8  class  cls
145, 13cfv 5570 . . . . . . 7  class  ( cls `  j )
1512, 14cfv 5570 . . . . . 6  class  ( ( cls `  j ) `
 ( x  \  { y } ) )
169, 15wcel 1823 . . . . 5  wff  y  e.  ( ( cls `  j
) `  ( x  \  { y } ) )
1716, 8cab 2439 . . . 4  class  { y  |  y  e.  ( ( cls `  j
) `  ( x  \  { y } ) ) }
184, 7, 17cmpt 4497 . . 3  class  ( x  e.  ~P U. j  |->  { y  |  y  e.  ( ( cls `  j ) `  (
x  \  { y } ) ) } )
192, 3, 18cmpt 4497 . 2  class  ( j  e.  Top  |->  ( x  e.  ~P U. j  |->  { y  |  y  e.  ( ( cls `  j ) `  (
x  \  { y } ) ) } ) )
201, 19wceq 1398 1  wff  limPt  =  ( j  e.  Top  |->  ( x  e.  ~P U. j  |->  { y  |  y  e.  ( ( cls `  j ) `
 ( x  \  { y } ) ) } ) )
Colors of variables: wff setvar class
This definition is referenced by:  lpfval  19809
  Copyright terms: Public domain W3C validator