All subsets of a set $X$ (its power set)

Example · Undergraduate

Terms

Term	This example	Why
topology	✓	The power set of $X$ is a topology on $X$: the discrete topology, in which every set is open.
σ-algebra	✓	The power set of $X$ is a σ-algebra on $X$, because it contains every subset of $X$, so it is closed under every set operation.

Distinctions using this example

• Topology vs. σ-algebra

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