A family of sets is called σ-discrete when it is a union of countably many discrete collections, where a family  of subsets of a space  is called discrete, when every point of  has a neighborhood that intersects at most one member of
A collection of sets is considered σ-discrete if it can be expressed as a union of countably many discrete families. A set family in a space is deemed discrete when each point within the space has a neighborhood intersecting with at most one element.