Definition:Subfamily

Definition

Let $I$ and $S$ be sets.

Let $x: I \to S$ be an indexing function for $S$.

Let $\family {x_i}_{i \mathop \in I}$ be a family indexed by $I$.

Let $J \subseteq I$ be a subset of $I$.

The family $\family {x_j}_{j \mathop \in J}$ indexed by $J$ is known as a subfamily of $\family {x_i}_{i \mathop \in I}$.

Sources

There are no source works cited for this page. In particular: The concept was used in passing by 1967: George McCarty: Topology: An Introduction with Application to Topological Groups, but the concept of "family" is not explicitly mentioned in that work at all. No other work I've seen has even mentioned the concept of "subfamily". Request that this page stay in place despite no sources being available, unless someone can suggest a way to restructure this direction of thought. Source citations are highly desirable, and mandatory for all definition pages. Definition pages whose content is wholly or partly unsourced are in danger of having such content deleted. To discuss this page in more detail, feel free to use the talk page.