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Mirrors > Home > MPE Home > Th. List > df-kq | Structured version Visualization version GIF version |
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.) |
Ref | Expression |
---|---|
df-kq | ⊢ KQ = (𝑗 ∈ Top ↦ (𝑗 qTop (𝑥 ∈ ∪ 𝑗 ↦ {𝑦 ∈ 𝑗 ∣ 𝑥 ∈ 𝑦}))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ckq 21874 | . 2 class KQ | |
2 | vj | . . 3 setvar 𝑗 | |
3 | ctop 21075 | . . 3 class Top | |
4 | 2 | cv 1655 | . . . 4 class 𝑗 |
5 | vx | . . . . 5 setvar 𝑥 | |
6 | 4 | cuni 4660 | . . . . 5 class ∪ 𝑗 |
7 | vy | . . . . . . 7 setvar 𝑦 | |
8 | 5, 7 | wel 2165 | . . . . . 6 wff 𝑥 ∈ 𝑦 |
9 | 8, 7, 4 | crab 3121 | . . . . 5 class {𝑦 ∈ 𝑗 ∣ 𝑥 ∈ 𝑦} |
10 | 5, 6, 9 | cmpt 4954 | . . . 4 class (𝑥 ∈ ∪ 𝑗 ↦ {𝑦 ∈ 𝑗 ∣ 𝑥 ∈ 𝑦}) |
11 | cqtop 16523 | . . . 4 class qTop | |
12 | 4, 10, 11 | co 6910 | . . 3 class (𝑗 qTop (𝑥 ∈ ∪ 𝑗 ↦ {𝑦 ∈ 𝑗 ∣ 𝑥 ∈ 𝑦})) |
13 | 2, 3, 12 | cmpt 4954 | . 2 class (𝑗 ∈ Top ↦ (𝑗 qTop (𝑥 ∈ ∪ 𝑗 ↦ {𝑦 ∈ 𝑗 ∣ 𝑥 ∈ 𝑦}))) |
14 | 1, 13 | wceq 1656 | 1 wff KQ = (𝑗 ∈ Top ↦ (𝑗 qTop (𝑥 ∈ ∪ 𝑗 ↦ {𝑦 ∈ 𝑗 ∣ 𝑥 ∈ 𝑦}))) |
Colors of variables: wff setvar class |
This definition is referenced by: kqval 21907 kqtop 21926 kqf 21928 |
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