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

 * Inclusion Mappings to Topological Sum from Components, in which it is demonstrated that the topology $\tau_3$ has the property that it is the finest topology on $Z$ such that the inclusion mappings from $\struct {X, \tau_1}$ and $\struct {Y, \tau_2}$ to $\struct {Z, \tau_3}$ are continuous.