For example, a cross is not a manifold; however, it can be expressed as the union of four 1-manifolds. In my opinion, this is somehow more "tractable" than other non-manifold objects like the union of a line and a region. I am particularly interested in the union of manifolds of the same dimensions.
My questions are:
- What are their name?
- What are some properties of this kind of objects? Are they considered similar to manifolds?
Your answer doesn't have to be complete in any sense. Any help will be appreciated!