Category:Partition Topology

From ProofWiki
Jump to navigation Jump to search

This category contains results about Partition Topology.


Let $S$ be a set.

Let $\mathcal P$ be a partition of $S$.

Let $\tau$ be the set of subsets of $S$ defined as:

$a \in \tau \iff a$ is the union of sets of $\mathcal P$


Then $\tau$ is a partition topology on $S$, and $\left({S, \tau}\right)$ is a partition (topological) space.