Neighborhood
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The neighborhood of a point is an open set containing that point.
Neighborhood is a college-level concept that would be first encountered in a topology course covering point-set topology.
Prerequisites
| Open Set: | An open set is a set for which every point in the set has a neighborhood lying in the set. An open set is the complement of a closed set and. An open interval is an example of an open set. |
| Topology: | (1) As a branch of mathematics, topology is the mathematical study of object's properties that are preserved through deformations, twistings, and stretchings. (2) As a set, a topology is a set along with a collection of subsets that satisfy several defining properties. |