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Definition df-kq 21478
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 ∈ Top ↦ (𝑗 qTop (𝑥 𝑗 ↦ {𝑦𝑗𝑥𝑦})))
Distinct variable group:   𝑥,𝑗,𝑦

Detailed syntax breakdown of Definition df-kq
StepHypRef Expression
1 ckq 21477 . 2 class KQ
2 vj . . 3 setvar 𝑗
3 ctop 20679 . . 3 class Top
42cv 1480 . . . 4 class 𝑗
5 vx . . . . 5 setvar 𝑥
64cuni 4427 . . . . 5 class 𝑗
7 vy . . . . . . 7 setvar 𝑦
85, 7wel 1989 . . . . . 6 wff 𝑥𝑦
98, 7, 4crab 2913 . . . . 5 class {𝑦𝑗𝑥𝑦}
105, 6, 9cmpt 4720 . . . 4 class (𝑥 𝑗 ↦ {𝑦𝑗𝑥𝑦})
11 cqtop 16144 . . . 4 class qTop
124, 10, 11co 6635 . . 3 class (𝑗 qTop (𝑥 𝑗 ↦ {𝑦𝑗𝑥𝑦}))
132, 3, 12cmpt 4720 . 2 class (𝑗 ∈ Top ↦ (𝑗 qTop (𝑥 𝑗 ↦ {𝑦𝑗𝑥𝑦})))
141, 13wceq 1481 1 wff KQ = (𝑗 ∈ Top ↦ (𝑗 qTop (𝑥 𝑗 ↦ {𝑦𝑗𝑥𝑦})))
Colors of variables: wff setvar class
This definition is referenced by:  kqval  21510  kqtop  21529  kqf  21531
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