The Borel sets of $\reals$

Example · Graduate

The smallest σ-algebra on $\reals$ that contains every open interval.

Terms

Term	This example	Why
σ-algebra	✓	The Borel sets of $\reals$ form a σ-algebra: the smallest σ-algebra that contains the open sets.
topology	✗	Every set is a union of one-point sets, which are Borel, but not every set is Borel. So the Borel sets are not closed under arbitrary unions.

Distinctions using this example

• Topology vs. σ-algebra

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