Topological spaces and open sets
General · Mathematics
Study notes
Q: Is {{},{a},{a,b}} a topology on X = {a,b}? What about {{},{a}}? {{},{a},{a,b}}: ∅,X ✓; unions: {a}∪{a,b} ✓; intersections ✓: TOPOLOGY! {{},{a}}: missing X = {a,b}: NOT a topology! (Sierpinski-like!) Discrete: {{},{a},{b},{a,b}}: all subsets!