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 ∈ TopSp → 𝐴 = ∪ 𝐽 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | istps.a | ⊢ 𝐴 = ( Base ‘ 𝐾 ) | |
2 | istps.j | ⊢ 𝐽 = ( TopOpen ‘ 𝐾 ) | |
3 | 1 2 | istps2 | ⊢ ( 𝐾 ∈ TopSp ↔ ( 𝐽 ∈ Top ∧ 𝐴 = ∪ 𝐽 ) ) |
4 | 3 | simprbi | ⊢ ( 𝐾 ∈ TopSp → 𝐴 = ∪ 𝐽 ) |