Definition:Expansion of Topology
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Definition
Let $S$ be a set.
Let $\tau_1$ and $\tau_2$ be topologies on $S$ such that $\tau_1 \subseteq \tau_2$.
Then $\tau_2$ is an expansion of $\tau_1$.
Also see
By definition, it can be seen that $\tau_2$ is an expansion of $\tau_1$ if and only if $\tau_1$ is coarser than $\tau_2$.
That is, if and only if $\tau_2$ is finer than $\tau_1$.
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $2$: Separation Axioms: Functions, Products, and Subspaces