# Category:Isolated Points

This category contains results about Isolated Points in the context of Topology.

Definitions specific to this category can be found in Definitions/Isolated Points.

Let $T = \left({S, \tau}\right)$ be a topological space.

### Isolated Point of Subset

$x \in H$ is an **isolated point of $H$** if and only if:

- $\exists U \in \tau: U \cap H = \left\{{x}\right\}$

That is, if and only if there exists an open set of $T$ containing no points of $H$ other than $x$.

### Isolated Point of Space

When $H = S$ the definition applies to the entire topological space $T = \left({S, \tau}\right)$:

$x \in S$ is an **isolated point of $T$** if and only if:

- $\exists U \in \tau: U = \left\{{x}\right\}$

That is, if and only if there exists an open set of $T$ containing no points of $S$ other than $x$.

## Subcategories

This category has the following 3 subcategories, out of 3 total.

## Pages in category "Isolated Points"

The following 13 pages are in this category, out of 13 total.