Definition df-kq 23579

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 23578	. 2 class KQ
2		vj	. . 3 setvar 𝑗
3		ctop 22778	. . 3 class Top
4	2	cv 1539	. . . 4 class 𝑗
5		vx	. . . . 5 setvar 𝑥
6	4	cuni 4858	. . . . 5 class ∪ 𝑗
7		vy	. . . . . . 7 setvar 𝑦
8	5, 7	wel 2110	. . . . . 6 wff 𝑥 ∈ 𝑦
9	8, 7, 4	crab 3394	. . . . 5 class {𝑦 ∈ 𝑗 ∣ 𝑥 ∈ 𝑦}
10	5, 6, 9	cmpt 5173	. . . 4 class (𝑥 ∈ ∪ 𝑗 ↦ {𝑦 ∈ 𝑗 ∣ 𝑥 ∈ 𝑦})
11		cqtop 17407	. . . 4 class qTop
12	4, 10, 11	co 7349	. . 3 class (𝑗 qTop (𝑥 ∈ ∪ 𝑗 ↦ {𝑦 ∈ 𝑗 ∣ 𝑥 ∈ 𝑦}))
13	2, 3, 12	cmpt 5173	. 2 class (𝑗 ∈ Top ↦ (𝑗 qTop (𝑥 ∈ ∪ 𝑗 ↦ {𝑦 ∈ 𝑗 ∣ 𝑥 ∈ 𝑦})))
14	1, 13	wceq 1540	1 wff KQ = (𝑗 ∈ Top ↦ (𝑗 qTop (𝑥 ∈ ∪ 𝑗 ↦ {𝑦 ∈ 𝑗 ∣ 𝑥 ∈ 𝑦})))

This definition is referenced by:  kqval  23611  kqtop  23630  kqf  23632