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Mirrors > Home > ILE Home > Th. List > df-topn | GIF version |
Description: Define the topology extractor function. This differs from df-tset 12554 when a structure has been restricted using df-iress 12469; 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.) |
Ref | Expression |
---|---|
df-topn | ⊢ TopOpen = (𝑤 ∈ V ↦ ((TopSet‘𝑤) ↾t (Base‘𝑤))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ctopn 12688 | . 2 class TopOpen | |
2 | vw | . . 3 setvar 𝑤 | |
3 | cvv 2737 | . . 3 class V | |
4 | 2 | cv 1352 | . . . . 5 class 𝑤 |
5 | cts 12541 | . . . . 5 class TopSet | |
6 | 4, 5 | cfv 5216 | . . . 4 class (TopSet‘𝑤) |
7 | cbs 12461 | . . . . 5 class Base | |
8 | 4, 7 | cfv 5216 | . . . 4 class (Base‘𝑤) |
9 | crest 12687 | . . . 4 class ↾t | |
10 | 6, 8, 9 | co 5874 | . . 3 class ((TopSet‘𝑤) ↾t (Base‘𝑤)) |
11 | 2, 3, 10 | cmpt 4064 | . 2 class (𝑤 ∈ V ↦ ((TopSet‘𝑤) ↾t (Base‘𝑤))) |
12 | 1, 11 | wceq 1353 | 1 wff TopOpen = (𝑤 ∈ V ↦ ((TopSet‘𝑤) ↾t (Base‘𝑤))) |
Colors of variables: wff set class |
This definition is referenced by: topnfn 12692 topnvalg 12699 |
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