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Definition df-topon 20764
Description: Define the function that associates with a set the set of topologies on it. (Contributed by Stefan O'Rear, 31-Jan-2015.)
Assertion
Ref Expression
df-topon TopOn = (𝑏 ∈ V ↦ {𝑗 ∈ Top ∣ 𝑏 = 𝑗})
Distinct variable group:   𝑗,𝑏

Detailed syntax breakdown of Definition df-topon
StepHypRef Expression
1 ctopon 20763 . 2 class TopOn
2 vb . . 3 setvar 𝑏
3 cvv 3231 . . 3 class V
42cv 1522 . . . . 5 class 𝑏
5 vj . . . . . . 7 setvar 𝑗
65cv 1522 . . . . . 6 class 𝑗
76cuni 4468 . . . . 5 class 𝑗
84, 7wceq 1523 . . . 4 wff 𝑏 = 𝑗
9 ctop 20746 . . . 4 class Top
108, 5, 9crab 2945 . . 3 class {𝑗 ∈ Top ∣ 𝑏 = 𝑗}
112, 3, 10cmpt 4762 . 2 class (𝑏 ∈ V ↦ {𝑗 ∈ Top ∣ 𝑏 = 𝑗})
121, 11wceq 1523 1 wff TopOn = (𝑏 ∈ V ↦ {𝑗 ∈ Top ∣ 𝑏 = 𝑗})
Colors of variables: wff setvar class
This definition is referenced by:  istopon  20765  funtopon  20773  toponsspwpw  20774  dmtopon  20775
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