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Definition df-kq 17718
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 17717 . 2  class KQ
2 vj . . 3  set  j
3 ctop 16950 . . 3  class  Top
42cv 1651 . . . 4  class  j
5 vx . . . . 5  set  x
64cuni 4007 . . . . 5  class  U. j
7 vy . . . . . . 7  set  y
85, 7wel 1726 . . . . . 6  wff  x  e.  y
98, 7, 4crab 2701 . . . . 5  class  { y  e.  j  |  x  e.  y }
105, 6, 9cmpt 4258 . . . 4  class  ( x  e.  U. j  |->  { y  e.  j  |  x  e.  y } )
11 cqtop 13721 . . . 4  class qTop
124, 10, 11co 6073 . . 3  class  ( j qTop  ( x  e.  U. j  |->  { y  e.  j  |  x  e.  y } ) )
132, 3, 12cmpt 4258 . 2  class  ( j  e.  Top  |->  ( j qTop  ( x  e.  U. j  |->  { y  e.  j  |  x  e.  y } ) ) )
141, 13wceq 1652 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  17750  kqtop  17769  kqf  17771
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