Description: The base set of a topological space. (Contributed by FL, 27-Jun-2014)
Ref | Expression | ||
---|---|---|---|
Hypotheses | istps.a | |- A = ( Base ` K ) |
|
istps.j | |- J = ( TopOpen ` K ) |
||
Assertion | tpsuni | |- ( K e. TopSp -> A = U. J ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | istps.a | |- A = ( Base ` K ) |
|
2 | istps.j | |- J = ( TopOpen ` K ) |
|
3 | 1 2 | istps2 | |- ( K e. TopSp <-> ( J e. Top /\ A = U. J ) ) |
4 | 3 | simprbi | |- ( K e. TopSp -> A = U. J ) |