Lebesgue's number lemma
Given a cover of a compact metric space, all small subsets are subset of some cover set / From Wikipedia, the free encyclopedia
In topology, the Delta number, is a useful tool in the study of compact metric spaces. It states:
- If the metric space
is compact and an open cover of
is given, then there exists a number
such that every subset of
having diameter less than
is contained in some member of the cover.
Such a number is called a Delta number of this cover. The notion of a Delta number itself is useful in other applications as well.