Definition:Zero Dimensional Space/Linguistic Note

Linguistic Note on Zero Dimensional Space

The thinking behind applying the term zero dimensional to the concept of a zero dimensional space arises from the idea of the small inductive dimension in the context of the topological space.

The small inductive dimension of a topological space is defined to be $1$ greater than the small inductive dimension of its boundary.

By Set is Clopen iff Boundary is Empty, a topological space with a basis whose sets are all clopen has no boundary.

Thus it follows that such a topological space is considered to be zero dimensional.

Sources

• Henno Brandsma (https://math.stackexchange.com/users/4280/henno-brandsma), What is the reason for the term "zero dimensional" in the context of topology?, URL (version: 2020-05-23): https://math.stackexchange.com/q/3687759