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Mirrors > Home > MPE Home > Th. List > df-topon | Structured version Visualization version GIF version |
Description: Define the function that associates with a set the set of topologies on it. (Contributed by Stefan O'Rear, 31-Jan-2015.) |
Ref | Expression |
---|---|
df-topon | ⊢ TopOn = (𝑏 ∈ V ↦ {𝑗 ∈ Top ∣ 𝑏 = ∪ 𝑗}) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ctopon 22049 | . 2 class TopOn | |
2 | vb | . . 3 setvar 𝑏 | |
3 | cvv 3431 | . . 3 class V | |
4 | 2 | cv 1541 | . . . . 5 class 𝑏 |
5 | vj | . . . . . . 7 setvar 𝑗 | |
6 | 5 | cv 1541 | . . . . . 6 class 𝑗 |
7 | 6 | cuni 4845 | . . . . 5 class ∪ 𝑗 |
8 | 4, 7 | wceq 1542 | . . . 4 wff 𝑏 = ∪ 𝑗 |
9 | ctop 22032 | . . . 4 class Top | |
10 | 8, 5, 9 | crab 3070 | . . 3 class {𝑗 ∈ Top ∣ 𝑏 = ∪ 𝑗} |
11 | 2, 3, 10 | cmpt 5162 | . 2 class (𝑏 ∈ V ↦ {𝑗 ∈ Top ∣ 𝑏 = ∪ 𝑗}) |
12 | 1, 11 | wceq 1542 | 1 wff TopOn = (𝑏 ∈ V ↦ {𝑗 ∈ Top ∣ 𝑏 = ∪ 𝑗}) |
Colors of variables: wff setvar class |
This definition is referenced by: istopon 22051 funtopon 22059 toponsspwpw 22061 dmtopon 22062 |
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