Definition:Empty Topological Space

Definition
Let $\varnothing$ denote the empty set.

The topological space $\struct {\O, \set \O}$ is called the empty topological space.

Also known as
The empty topological space is also known as the empty space if the context of topology is established.

Also see

 * Empty Set Satisfies Topology Axioms, demonstrating that $\struct {\O, \set \O}$ is indeed a topological space.