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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 22304 | . 2 class KQ | |
2 | vj | . . 3 setvar 𝑗 | |
3 | ctop 21504 | . . 3 class Top | |
4 | 2 | cv 1535 | . . . 4 class 𝑗 |
5 | vx | . . . . 5 setvar 𝑥 | |
6 | 4 | cuni 4841 | . . . . 5 class ∪ 𝑗 |
7 | vy | . . . . . . 7 setvar 𝑦 | |
8 | 5, 7 | wel 2114 | . . . . . 6 wff 𝑥 ∈ 𝑦 |
9 | 8, 7, 4 | crab 3145 | . . . . 5 class {𝑦 ∈ 𝑗 ∣ 𝑥 ∈ 𝑦} |
10 | 5, 6, 9 | cmpt 5149 | . . . 4 class (𝑥 ∈ ∪ 𝑗 ↦ {𝑦 ∈ 𝑗 ∣ 𝑥 ∈ 𝑦}) |
11 | cqtop 16779 | . . . 4 class qTop | |
12 | 4, 10, 11 | co 7159 | . . 3 class (𝑗 qTop (𝑥 ∈ ∪ 𝑗 ↦ {𝑦 ∈ 𝑗 ∣ 𝑥 ∈ 𝑦})) |
13 | 2, 3, 12 | cmpt 5149 | . 2 class (𝑗 ∈ Top ↦ (𝑗 qTop (𝑥 ∈ ∪ 𝑗 ↦ {𝑦 ∈ 𝑗 ∣ 𝑥 ∈ 𝑦}))) |
14 | 1, 13 | wceq 1536 | 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 22337 kqtop 22356 kqf 22358 |
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