Definition df-kq 23689

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 ↦ {𝑦 ∈ 𝑗 ∣ 𝑥 ∈ 𝑦})))

Distinct variable group:   𝑥,𝑗,𝑦

Detailed syntax breakdown of Definition df-kq

Step	Hyp	Ref	Expression
1		ckq 23688	. 2 class KQ
2		vj	. . 3 setvar 𝑗
3		ctop 22886	. . 3 class Top
4	2	cv 1533	. . . 4 class 𝑗
5		vx	. . . . 5 setvar 𝑥
6	4	cuni 4913	. . . . 5 class ∪ 𝑗
7		vy	. . . . . . 7 setvar 𝑦
8	5, 7	wel 2100	. . . . . 6 wff 𝑥 ∈ 𝑦
9	8, 7, 4	crab 3419	. . . . 5 class {𝑦 ∈ 𝑗 ∣ 𝑥 ∈ 𝑦}
10	5, 6, 9	cmpt 5236	. . . 4 class (𝑥 ∈ ∪ 𝑗 ↦ {𝑦 ∈ 𝑗 ∣ 𝑥 ∈ 𝑦})
11		cqtop 17518	. . . 4 class qTop
12	4, 10, 11	co 7424	. . 3 class (𝑗 qTop (𝑥 ∈ ∪ 𝑗 ↦ {𝑦 ∈ 𝑗 ∣ 𝑥 ∈ 𝑦}))
13	2, 3, 12	cmpt 5236	. 2 class (𝑗 ∈ Top ↦ (𝑗 qTop (𝑥 ∈ ∪ 𝑗 ↦ {𝑦 ∈ 𝑗 ∣ 𝑥 ∈ 𝑦})))
14	1, 13	wceq 1534	1 wff KQ = (𝑗 ∈ Top ↦ (𝑗 qTop (𝑥 ∈ ∪ 𝑗 ↦ {𝑦 ∈ 𝑗 ∣ 𝑥 ∈ 𝑦})))

This definition is referenced by:  kqval  23721  kqtop  23740  kqf  23742