Proof That Every Closed and Bounded Interval With the Absolute Value Topology is Compact
Theorem
Every closed and bounded interval
of
with the absolute value topology is compact.
Proof
The proof is done with the aid of the Heine - Borel Theorem:
Letbe a closed and interval inand let
be a collection of sets open in satisfying
then we can select a finite number of the
say
satisfying
Hence every open coverofhas a finite subcover
andis compact.
