Definition:Particular Point Topology/Uncountable

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

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

Let $T = \struct {S, \tau_p}$ be the particular point space on $S$ by $p$.

Let $S$ be uncountable.

Then $\tau_p$ is an uncountable particular point topology, and $\struct {S, \tau_p}$ is an uncountable particular point space.

Also see

 * Definition:Finite Particular Point Topology
 * Definition:Countable Particular Point Topology