# Definition:Excluded Point Topology/Infinite

## Definition

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

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

Let $T = \left({S, \tau_{\bar p}}\right)$ be the excluded point space on $S$ by $p$.

Let $S$ be infinite.

Then $\tau_{\bar p}$ is an infinite excluded point topology, and $\left({S, \tau_{\bar p}}\right)$ is a infinite excluded point space.

### Countable Excluded Point Topology

Let $S$ be countably infinite.

Then $\tau_{\bar p}$ is a countable excluded point topology, and $\struct {S, \tau_{\bar p} }$ is a countable excluded point space.

### Uncountable Excluded Point Topology

Let $S$ be uncountable.

Then $\tau_{\bar p}$ is an uncountable excluded point topology, and $\struct {S, \tau_{\bar p} }$ is an uncountable excluded point space.

## Also see

• Results about excluded point topologies can be found here.