# Contents

## Definition

Given a set $X_i$, $i \in I$ of topological space, then their disjoint union space $\underset{i \in I}{\sqcup} X_i$ is the topological space whose underlying set is the disjoint union of the underlying sets of the $X_i$, and whose open subsets are precisely the disjoint unions of the open subsets of the $X_i$.

More abstractly, this is the coproduct in the category Top of topological spaces.

examples of universal constructions of topological spaces:

$\phantom{AAAA}$limits$\phantom{AAAA}$colimits
$\,$ point space$\,$$\,$ empty space $\,$
$\,$ product topological space $\,$$\,$ disjoint union topological space $\,$
$\,$ topological subspace $\,$$\,$ quotient topological space $\,$
$\,$ fiber space $\,$$\,$ space attachment $\,$
$\,$ mapping cocylinder, mapping cocone $\,$$\,$ mapping cylinder, mapping cone, mapping telescope $\,$
$\,$ cell complex, CW-complex $\,$

Last revised on May 14, 2017 at 07:23:57. See the history of this page for a list of all contributions to it.