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 letbe a nested local base at a pointLetbe a sequence such thatThenconverges to
Proof
Letbe an open set containing
is a local base athenceexists such that
Setsare nested if
Hence for anywithand sincewe have
Hence