The Relationship Between Topological and Measurable Spaces

Remark

Remark. The notion of a measurable space $(X,\mathcal{X})$ (and of a measurable function) is superficially similar to that of a topological space $(X,\tau )$ (and of a continuous function); the topology $\tau$ contains $\varnothing$ and $X$ just as the σ-algebra $\mathcal{X}$ does, but is now closed under arbitrary unions and finite intersections, rather than countable unions, countable intersections, and complements. The two spaces are linked to each other by the Borel σ-algebra construction.

References

Tao, T. — An epsilon of room-pages from year three of a mathematical blog.pdf, Remark 1.1.3