Definition:Discrete Set of Subsets
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Definition
Let $T = \struct {S, \tau}$ be a topological space.
Let $\FF$ be a set of subsets of $S$.
Then $\FF$ is discrete if and only if each element of $S$ has a neighborhood which intersects at most one of the sets in $\FF$.
Sources
- 1955: John L. Kelley: General Topology: Chapter $4$: Embedding and Metrization
- 1970: Stephen Willard: General Topology: Chapter $6$: Compactness: $\S20$: Paracompactness: Definition $22.2$
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.): Part $\text {III}$: Metrization Theory: Conjectures and Counterexamples: Screenable Spaces