# Definition:Trivial Topological Space

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## Definition

A **trivial topological space** is a topological space with only one element.

The open sets of a **trivial topological space** $T = \left({\left\{{s}\right\}, \tau}\right)$ are $\varnothing$ and $\left\{{s}\right\}$.

## Also see

- Definition:Indiscrete Topology, also known as a
**trivial topology**.

This is not the same as a **trivial topological space** unless its underlying set is a singleton.

- Results about
**the trivial topological space**can be found here.