A definition of topological sum
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 topological sum
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 any family of topological spaces, \(\{T_\alpha\}\) where \(\{\alpha\}\) is any possibly uncountable indexes set, the disjoint union, \(\coprod_\alpha T_\alpha\), with the topology such that any subset, \(S \subseteq \coprod_\alpha T_\alpha\) is open if and only if \(S \cap T_\alpha\) is open for each \(\alpha\), often denoted like \(T_1 + T_2\) when the indexes set is finite
