locally closed
- A subset of a topological space is said to be locally closed if it is the intersection
of an open and a closed subset.
The following result provides some definitions:
- The following are equivalent:
- 1.
is locally closed in .
- 2.
Each point in has an open neighborhood such that is closed in (with the subspace topology).
- 3.
is open in its closure
(with the subspace topology).