MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-topn Structured version   Visualization version   GIF version

Definition df-topn 16289
Description: Define the topology extractor function. This differs from df-tset 16172 when a structure has been restricted using df-ress 16076; 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 16287 . 2 class TopOpen
2 vw . . 3 setvar 𝑤
3 cvv 3391 . . 3 class V
42cv 1636 . . . . 5 class 𝑤
5 cts 16159 . . . . 5 class TopSet
64, 5cfv 6101 . . . 4 class (TopSet‘𝑤)
7 cbs 16068 . . . . 5 class Base
84, 7cfv 6101 . . . 4 class (Base‘𝑤)
9 crest 16286 . . . 4 class t
106, 8, 9co 6874 . . 3 class ((TopSet‘𝑤) ↾t (Base‘𝑤))
112, 3, 10cmpt 4923 . 2 class (𝑤 ∈ V ↦ ((TopSet‘𝑤) ↾t (Base‘𝑤)))
121, 11wceq 1637 1 wff TopOpen = (𝑤 ∈ V ↦ ((TopSet‘𝑤) ↾t (Base‘𝑤)))
Colors of variables: wff setvar class
This definition is referenced by:  topnfn  16291  topnval  16300
  Copyright terms: Public domain W3C validator