- Topological space is defined more generally than topological manifolds. So all topological manifolds are topological spaces. But some topological spaces are not topological manifolds.
What are examples of topological spaces that are not topological manifolds?
- Topological groups are logically the combination of groups and topological spaces, i.e. they are group and topological spaces at the same time, s.t. the continuity condition for the group operations connect these two structures together and consequently they are not independent from each other. So topological groups are also topological spaces.
What are examples of topological groups that are combination of groups and topological manifolds?
Lie groups are topological groups. Are finite groups also topological groups?