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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 21496 | . 2 class KQ | |
2 | vj | . . 3 setvar 𝑗 | |
3 | ctop 20698 | . . 3 class Top | |
4 | 2 | cv 1482 | . . . 4 class 𝑗 |
5 | vx | . . . . 5 setvar 𝑥 | |
6 | 4 | cuni 4436 | . . . . 5 class ∪ 𝑗 |
7 | vy | . . . . . . 7 setvar 𝑦 | |
8 | 5, 7 | wel 1991 | . . . . . 6 wff 𝑥 ∈ 𝑦 |
9 | 8, 7, 4 | crab 2916 | . . . . 5 class {𝑦 ∈ 𝑗 ∣ 𝑥 ∈ 𝑦} |
10 | 5, 6, 9 | cmpt 4729 | . . . 4 class (𝑥 ∈ ∪ 𝑗 ↦ {𝑦 ∈ 𝑗 ∣ 𝑥 ∈ 𝑦}) |
11 | cqtop 16163 | . . . 4 class qTop | |
12 | 4, 10, 11 | co 6650 | . . 3 class (𝑗 qTop (𝑥 ∈ ∪ 𝑗 ↦ {𝑦 ∈ 𝑗 ∣ 𝑥 ∈ 𝑦})) |
13 | 2, 3, 12 | cmpt 4729 | . 2 class (𝑗 ∈ Top ↦ (𝑗 qTop (𝑥 ∈ ∪ 𝑗 ↦ {𝑦 ∈ 𝑗 ∣ 𝑥 ∈ 𝑦}))) |
14 | 1, 13 | wceq 1483 | 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 21529 kqtop 21548 kqf 21550 |
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