# Definition:Topological Sum

## Definition

Let $\struct {X, \tau_1}$ and $\struct {Y, \tau_2}$ be topological spaces.

The topological sum $\struct {Z, \tau_3}$ of $X$ and $Y$ is defined as:

$Z = X \sqcup Y$

where:

$X \sqcup Y$ denotes the disjoint union of $X$ and $Y$
$\tau_3$ is the topology generated by $\tau_1$ and $\tau_2$.

## Also see

• Results about topological sum can be found here.