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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 21306 | . 2 class KQ | |
2 | vj | . . 3 setvar 𝑗 | |
3 | ctop 20517 | . . 3 class Top | |
4 | 2 | cv 1474 | . . . 4 class 𝑗 |
5 | vx | . . . . 5 setvar 𝑥 | |
6 | 4 | cuni 4372 | . . . . 5 class ∪ 𝑗 |
7 | vy | . . . . . . 7 setvar 𝑦 | |
8 | 5, 7 | wel 1978 | . . . . . 6 wff 𝑥 ∈ 𝑦 |
9 | 8, 7, 4 | crab 2900 | . . . . 5 class {𝑦 ∈ 𝑗 ∣ 𝑥 ∈ 𝑦} |
10 | 5, 6, 9 | cmpt 4643 | . . . 4 class (𝑥 ∈ ∪ 𝑗 ↦ {𝑦 ∈ 𝑗 ∣ 𝑥 ∈ 𝑦}) |
11 | cqtop 15986 | . . . 4 class qTop | |
12 | 4, 10, 11 | co 6549 | . . 3 class (𝑗 qTop (𝑥 ∈ ∪ 𝑗 ↦ {𝑦 ∈ 𝑗 ∣ 𝑥 ∈ 𝑦})) |
13 | 2, 3, 12 | cmpt 4643 | . 2 class (𝑗 ∈ Top ↦ (𝑗 qTop (𝑥 ∈ ∪ 𝑗 ↦ {𝑦 ∈ 𝑗 ∣ 𝑥 ∈ 𝑦}))) |
14 | 1, 13 | wceq 1475 | 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 21339 kqtop 21358 kqf 21360 |
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