Thread: Demonstration of that the union of manifolds is not a mainfold

Hello.
I was looking for that demonstration, and I know how to start: As they aren't contain in each other I have to take a point in each one that it is not in the other one. So they (the points) will be in the union of both of the mainfolds. So I have to proove that the half point of them is not in the union. That's all.

Thank you so much (I hope you have understood my English, I am from Spain)

This question is more about topology than logic. You should send a private message to Plato or another moderator and ask him to move the thread. Or perhaps you can post this in the Analysis, Topology and Differential Geometry forum and make a note about it here.

If this question comes from a course in logic (and not topology), then please let us know. In this case, a definition of a manifold would be useful.

The line R is a manifold. But the union of two crossing lines is not.

You could also consider the disjoint union of two manifolds of different dimensions.

Originally Posted by Lolyta

Hello.
I was looking for that demonstration, and I know how to start: As they aren't contain in each other I have to take a point in each one that it is not in the other one. So they (the points) will be in the union of both of the mainfolds. So I have to proove that the half point of them is not in the union. That's all.

Thank you so much (I hope you have understood my English, I am from Spain)

You could take the union of a zero-dimensional submanifold of and .