A definition of disjoint union topology
Topics
About: topological space
The table of contents of this article
Starting Context
- The reader knows a definition of topological space.
Target Context
- The reader will have a definition of disjoint union topology.
Orientation
There is a list of definitions discussed so far in this site.
There is a list of propositions discussed so far in this site.
Main Body
1: Definition
For the set of any possibly uncountable number of topological spaces, \(\{T_\alpha\}\), and the disjoint union, \(\coprod_\alpha T_\alpha\), the topology such that any subset, \(S \subseteq \coprod_\alpha T_\alpha\), is open if and only if each \(S \cap T_\alpha\) is open
