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Definition df-kq 20633
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 20632 . 2  class KQ
2 vj . . 3  setvar  j
3 ctop 19841 . . 3  class  Top
42cv 1436 . . . 4  class  j
5 vx . . . . 5  setvar  x
64cuni 4213 . . . . 5  class  U. j
7 vy . . . . . . 7  setvar  y
85, 7wel 1868 . . . . . 6  wff  x  e.  y
98, 7, 4crab 2777 . . . . 5  class  { y  e.  j  |  x  e.  y }
105, 6, 9cmpt 4475 . . . 4  class  ( x  e.  U. j  |->  { y  e.  j  |  x  e.  y } )
11 cqtop 15353 . . . 4  class qTop
124, 10, 11co 6296 . . 3  class  ( j qTop  ( x  e.  U. j  |->  { y  e.  j  |  x  e.  y } ) )
132, 3, 12cmpt 4475 . 2  class  ( j  e.  Top  |->  ( j qTop  ( x  e.  U. j  |->  { y  e.  j  |  x  e.  y } ) ) )
141, 13wceq 1437 1  wff KQ  =  ( j  e.  Top  |->  ( j qTop  ( x  e. 
U. j  |->  { y  e.  j  |  x  e.  y } ) ) )
Colors of variables: wff setvar class
This definition is referenced by:  kqval  20665  kqtop  20684  kqf  20686
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