Open Covers of Topological Spaces
An open overs of a topological spaceis a collection of open setssuch that
Letbe the set of real numbers with topology induced by the absolute value metric.
is the set of open ballsThis set of open balls is an open cover because
The setis an open subcover.
An open coveris said to be finer or an improvement on some other open coverif for eachthere is somesuch that
Henceis an improvement of