Definition:Topological Sum

From ProofWiki
Jump to navigation Jump to search

Definition

Let $\left({X, \tau_1}\right)$ and $\left({Y, \tau_2}\right)$ be topological spaces.


The topological sum $\left({Z, \tau_3}\right)$ 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.


Sources