Separation axioms (T0-T4)
General · Mathematics
Study notes
Q: Is ℝ with usual topology Hausdorff (T2)? What about indiscrete? ℝ: x≠y: intervals (x-ε,x+ε), (y-ε,y+ε) disjoint (ε = |x-y|/3!): T2 ✓! Indiscrete {∅,X}: only opens: can't separate: NOT T1 (not even T0 if |X|>1!)! Metric spaces: always T4 (normal)! (T2: limits unique!)