# Category:Excluded Point Topology

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This category contains results about Excluded Point Topology.

Definitions specific to this category can be found in Definitions/Excluded Point Topology.

Let $S$ be a set which is non-empty.

Let $p \in S$ be some **particular point** of $S$.

We define a subset $\tau_{\bar p}$ of the power set $\mathcal P \left({S}\right)$ as:

- $\tau_{\bar p} = \left\{{A \subseteq S: p \notin A}\right\} \cup \left\{{S}\right\}$

That is, all the subsets of $S$ which do not include $p$, along with the set $S$.

Then $\tau_{\bar p}$ is a topology called the **excluded point topology on $S$ by $p$**, or just **an excluded point topology**.

## Subcategories

This category has the following 10 subcategories, out of 10 total.

### E

### S

## Pages in category "Excluded Point Topology"

The following 28 pages are in this category, out of 28 total.

### E

- Excluded Point Space is Compact
- Excluded Point Space is Connected
- Excluded Point Space is First-Countable
- Excluded Point Space is Locally Path-Connected
- Excluded Point Space is not Arc-Connected
- Excluded Point Space is not Irreducible
- Excluded Point Space is not Locally Arc-Connected
- Excluded Point Space is not Perfectly T4
- Excluded Point Space is Path-Connected
- Excluded Point Space is Scattered
- Excluded Point Space is Sequentially Compact
- Excluded Point Space is T0
- Excluded Point Space is T5
- Excluded Point Space is Ultraconnected
- Excluded Point Topology is not T3
- Excluded Point Topology is Open Extension Topology of Discrete Topology
- Excluded Point Topology is T4
- Excluded Point Topology is Topology