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To verify a collection τ is a topology on a finite set X, check three conditions: (1) confirm ∅ and X are in τ; (2) verify that the union of any subfamily of τ is in τ; and (3) verify that the intersection of any finite subfamily of τ is in τ.
Conditions: X is a finite set.; τ is a proposed collection of subsets of X.
3:05 – 5:00Watch this moment ↗
To verify a collection τ is a topology on a finite set X, check three conditions: (1) confirm ∅ and X are in τ; (2) verify that the union of any subfamily of τ is in τ; and (3) verify that the intersection of any finite subfamily of τ is in τ.
Conditions: X is a finite set.; τ is a proposed collection of subsets of X.
3:05 – 5:00Watch this moment ↗