Definition df-topn 12559

Description: Define the topology extractor function. This differs from df-tset 12476 when a structure has been restricted using df-ress 12402; in this case the TopSet component will still have a topology over the larger set, and this function fixes this by restricting the topology as well. (Contributed by Mario Carneiro, 13-Aug-2015.)

Assertion

Ref	Expression
df-topn	⊢ TopOpen = (𝑤 ∈ V ↦ ((TopSet‘𝑤) ↾t (Base‘𝑤)))

Detailed syntax breakdown of Definition df-topn

Step	Hyp	Ref	Expression
1		ctopn 12557	. 2 class TopOpen
2		vw	. . 3 setvar 𝑤
3		cvv 2726	. . 3 class V
4	2	cv 1342	. . . . 5 class 𝑤
5		cts 12463	. . . . 5 class TopSet
6	4, 5	cfv 5188	. . . 4 class (TopSet‘𝑤)
7		cbs 12394	. . . . 5 class Base
8	4, 7	cfv 5188	. . . 4 class (Base‘𝑤)
9		crest 12556	. . . 4 class ↾t
10	6, 8, 9	co 5842	. . 3 class ((TopSet‘𝑤) ↾t (Base‘𝑤))
11	2, 3, 10	cmpt 4043	. 2 class (𝑤 ∈ V ↦ ((TopSet‘𝑤) ↾t (Base‘𝑤)))
12	1, 11	wceq 1343	1 wff TopOpen = (𝑤 ∈ V ↦ ((TopSet‘𝑤) ↾t (Base‘𝑤)))

This definition is referenced by:  topnfn  12561  topnvalg  12568