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

Definition df-kq 17441
Description: Define the Kolmogorov quotient. This is a function on topologies which maps a topology to its quotient under the topological distinguishability map, which takes a point to the set of open sets that contain it. Two points are mapped to the same image under this function iff they are topologically indistinguishable. (Contributed by Mario Carneiro, 25-Aug-2015.)
Assertion
Ref Expression
df-kq  |- KQ  =  ( j  e.  Top  |->  ( j qTop  ( x  e. 
U. j  |->  { y  e.  j  |  x  e.  y } ) ) )
Distinct variable group:    x, j, y

Detailed syntax breakdown of Definition df-kq
StepHypRef Expression
1 ckq 17440 . 2  class KQ
2 vj . . 3  set  j
3 ctop 16687 . . 3  class  Top
42cv 1632 . . . 4  class  j
5 vx . . . . 5  set  x
64cuni 3864 . . . . 5  class  U. j
7 vy . . . . . . 7  set  y
85, 7wel 1702 . . . . . 6  wff  x  e.  y
98, 7, 4crab 2581 . . . . 5  class  { y  e.  j  |  x  e.  y }
105, 6, 9cmpt 4114 . . . 4  class  ( x  e.  U. j  |->  { y  e.  j  |  x  e.  y } )
11 cqtop 13455 . . . 4  class qTop
124, 10, 11co 5900 . . 3  class  ( j qTop  ( x  e.  U. j  |->  { y  e.  j  |  x  e.  y } ) )
132, 3, 12cmpt 4114 . 2  class  ( j  e.  Top  |->  ( j qTop  ( x  e.  U. j  |->  { y  e.  j  |  x  e.  y } ) ) )
141, 13wceq 1633 1  wff KQ  =  ( j  e.  Top  |->  ( j qTop  ( x  e. 
U. j  |->  { y  e.  j  |  x  e.  y } ) ) )
Colors of variables: wff set class
This definition is referenced by:  kqval  17473  kqtop  17492  kqf  17494
  Copyright terms: Public domain W3C validator