Definition:Expansion (Topology)

Definition

Let $X$ be a set.

Let $\vartheta_1$ and $\vartheta_2$ be topologies on $X$ such that $\vartheta_1 \subseteq \vartheta_2$.

Then $\vartheta_2$ is an expansion of $\vartheta_1$.

Also see

By definition, it can be seen that $\vartheta_2$ is an expansion of $\vartheta_1$ iff $\vartheta_1$ is coarser than $\vartheta_2$.

Alternatively, iff $\vartheta_2$ is finer than $\vartheta_1$.

Sources

• Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (1970)... (previous)... (next): $\text{I}: \ \S 2$: Functions, Products, and Subspaces