Description: Define the class of topological spaces (as extensible structures). (Contributed by Stefan O'Rear, 13-Aug-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | df-topsp | |- TopSp = { f | ( TopOpen ` f ) e. ( TopOn ` ( Base ` f ) ) } |
Step | Hyp | Ref | Expression |
---|---|---|---|
0 | ctps | |- TopSp |
|
1 | vf | |- f |
|
2 | ctopn | |- TopOpen |
|
3 | 1 | cv | |- f |
4 | 3 2 | cfv | |- ( TopOpen ` f ) |
5 | ctopon | |- TopOn |
|
6 | cbs | |- Base |
|
7 | 3 6 | cfv | |- ( Base ` f ) |
8 | 7 5 | cfv | |- ( TopOn ` ( Base ` f ) ) |
9 | 4 8 | wcel | |- ( TopOpen ` f ) e. ( TopOn ` ( Base ` f ) ) |
10 | 9 1 | cab | |- { f | ( TopOpen ` f ) e. ( TopOn ` ( Base ` f ) ) } |
11 | 0 10 | wceq | |- TopSp = { f | ( TopOpen ` f ) e. ( TopOn ` ( Base ` f ) ) } |