Definition:Nested Sequence

Definition

Let $\left \langle {S_k}\right \rangle$ be a sequence of sets such that either:

$\forall k \in \N: S_k \subseteq S_{k+1}$

or:

$\forall k \in \N: S_k \supseteq S_{k+1}$

Then $\left \langle {S_k}\right \rangle$ is a nested sequence of sets.

Sources

• Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (1970)... (previous)... (next): $\text{I}: \ \S 5$: Complete Metric Spaces