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

Example · Undergraduate

Terms

Term	This example	Why
topology	✓	The collection $\setdef{\emptyset, \setdef{1}, \setdef{1, 2}}$ is a topology on $\setdef{1, 2}$, because it contains $\emptyset$ and $\setdef{1, 2}$ and is closed under unions and intersections.
σ-algebra	✗	The collection $\setdef{\emptyset, \setdef{1}, \setdef{1, 2}}$ is not a σ-algebra on $\setdef{1, 2}$, because it does not contain $\setdef{2}$, the complement of $\setdef{1}$.

Distinctions using this example

• Topology vs. σ-algebra

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