Category:Partition Topology
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This category contains results about Partition Topology.
Let $S$ be a set.
Let $\PP$ 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 $\PP$
Then $\tau$ is a partition topology on $S$, and $\struct {S, \tau}$ is a partition (topological) space.
Subcategories
This category has the following 2 subcategories, out of 2 total.
D
- Deleted Integer Topology (6 P)
O
- Odd-Even Topology (6 P)
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