Topological Basis

up:: Topology

Given a set $X\ne \varnothing$, a topological basis $\mathcal{B}\subset \mathbb{P}(X)$ of $X$ is a family of subsets of $X$ which generate a Topology of $X$ through (arbitrary) unions of elements of $\mathcal{B}$.

It is analogous to a base in Linear Algebra, in which all elements in a vector space can be seen as a linear combination of basis vectors.

Note that The metric topology is generated by open balls.

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References

• Notas para um Curso de Física-Matemática, João Carlos Alves Barata. Cap. 27