- I was wondering if there is a concept of boundedness for subsets of a topological space?
If yes to 1, is it this one from Wiki
Elements of a Bornology B on a set X are called bounded sets and the pair (X, B) is called a bornological set.
For any topological space X, the set of subsets of X with compact closure is a Bornology.
- If yes to 2, does it coincide with boundedness in a metric space and in a topological vector space? How is it related to total boundedness in a uniform space?
Thanks and regards!