Definition df-topon 15035

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

Step	Hyp	Ref	Expression
1		ctopon 15034	. 2 class TopOn
2		vb	. . 3 setvar 𝑏
3		cvv 2821	. . 3 class V
4	2	cv 1401	. . . . 5 class 𝑏
5		vj	. . . . . . 7 setvar 𝑗
6	5	cv 1401	. . . . . 6 class 𝑗
7	6	cuni 3930	. . . . 5 class ∪ 𝑗
8	4, 7	wceq 1402	. . . 4 wff 𝑏 = ∪ 𝑗
9		ctop 15021	. . . 4 class Top
10	8, 5, 9	crab 2532	. . 3 class {𝑗 ∈ Top ∣ 𝑏 = ∪ 𝑗}
11	2, 3, 10	cmpt 4187	. 2 class (𝑏 ∈ V ↦ {𝑗 ∈ Top ∣ 𝑏 = ∪ 𝑗})
12	1, 11	wceq 1402	1 wff TopOn = (𝑏 ∈ V ↦ {𝑗 ∈ Top ∣ 𝑏 = ∪ 𝑗})

This definition is referenced by:  funtopon  15036  istopon  15037  toponsspwpwg  15046  dmtopon  15047