$\setdef{\emptyset, \setdef{1}, \setdef{2, 3}, \setdef{1, 2, 3}}$, on $X = \setdef{1, 2, 3}$

Example · Undergraduate

Terms

Term	This example	Why
topology	✓	The collection $\setdef{\emptyset, \setdef{1}, \setdef{2, 3}, \setdef{1, 2, 3}}$ is a topology on $\setdef{1, 2, 3}$, because it contains $\emptyset$ and $\setdef{1, 2, 3}$, and every union and intersection of its sets is in it.
σ-algebra	✓	The collection $\setdef{\emptyset, \setdef{1}, \setdef{2, 3}, \setdef{1, 2, 3}}$ is a σ-algebra on $\setdef{1, 2, 3}$, because it contains the complement of each of its sets, and every union of them.

Distinctions using this example

• Topology vs. σ-algebra

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