Coarseness Relation on Topologies is Partial Ordering
Let $X$ be a set.
Let $\mathbb T$ be the set of all topologies on $X$
Let $\le$ be the relation on $\mathbb T$:
Then $\le$ is a partial ordering on $\mathbb T$.
It follows directly from the definition of being coarser that:
- $\tau_1 \le \tau_2 \iff \tau_1 \subseteq \tau_2$