Basis and subbasis
General · Mathematics
Study notes
Q: Show open intervals form a basis for ℝ's topology. Is {(a,∞)} a basis? Every open U: union of intervals (x-ε,x+ε) ✓: BASIS! {(a,∞)}: finite intersections: (a,∞): can't get (0,1): NOT basis! But SUBBASIS: finite ∩ gives (a,b) = (a,∞)∩(-∞,b)... need (-∞,b) too! Subbasis: {(a,∞),(-∞,b)}: generates! (Basis: building blocks!)