topological space

Definition

A topological space $(X,\tau)$ is a set $X$ equipped with a topology $\tau$.

Notes

• topology is closed under arbitrary unions and finite intersections, whereas measurable space is closed under countable unions, countable intersections, and complements
• a Borel σ-algebra is generated by open sets of a topological space
• more abstractly, a topological space is a type of structure on a set
• the category, Top has topological spaces as objects and continuous functions as its morphisms

See also

• dependent type theory

References

1. https://ncatlab.org/nlab/show/topological+space
2. https://math.stackexchange.com/questions/1330649/difference-between-topology-and-sigma-algebra-axioms
3. https://ncatlab.org/nlab/show/Top