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Definition df-topn 16131
Description: Define the topology extractor function. This differs from df-tset 16007 when a structure has been restricted using df-ress 15912; 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
StepHypRef Expression
1 ctopn 16129 . 2 class TopOpen
2 vw . . 3 setvar 𝑤
3 cvv 3231 . . 3 class V
42cv 1522 . . . . 5 class 𝑤
5 cts 15994 . . . . 5 class TopSet
64, 5cfv 5926 . . . 4 class (TopSet‘𝑤)
7 cbs 15904 . . . . 5 class Base
84, 7cfv 5926 . . . 4 class (Base‘𝑤)
9 crest 16128 . . . 4 class t
106, 8, 9co 6690 . . 3 class ((TopSet‘𝑤) ↾t (Base‘𝑤))
112, 3, 10cmpt 4762 . 2 class (𝑤 ∈ V ↦ ((TopSet‘𝑤) ↾t (Base‘𝑤)))
121, 11wceq 1523 1 wff TopOpen = (𝑤 ∈ V ↦ ((TopSet‘𝑤) ↾t (Base‘𝑤)))
Colors of variables: wff setvar class
This definition is referenced by:  topnfn  16133  topnval  16142
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