Proof That a Nested Local Base at a Point of a Topological Space Contains a Sequence Converging to the Point
Theorem
Letbe a topological space and let
be a nested local base at a point
Let
be a sequence such that
Then
converges to
Proof
Letbe an open set containing
is a local base at
hence
exists such that
Setsare nested if
Hence for anywith
and since
we have
Hence