# Category:Partition Topology

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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**.

## Subcategories

This category has the following 2 subcategories, out of 2 total.

## Pages in category "Partition Topology"

The following 19 pages are in this category, out of 19 total.

### D

### P

- Partition of Singletons yields Discrete Topology
- Partition Space is Pseudometrizable
- Partition Topology is not Completely Hausdorff
- Partition Topology is not Hausdorff
- Partition Topology is not T0
- Partition Topology is not T1
- Partition Topology is T3
- Partition Topology is T3 1/2
- Partition Topology is T4
- Partition Topology is T5
- Partition Topology is Topology
- Partition Topology is Zero Dimensional