Ignoring boundary term in the action

[davidge]

What I mean is, "let the natural coordinates --just the label of the points of $\mathbb{R}^2 \times \mathbb{S}^2$-- be $(t,r, \theta, \phi)$. Now, let's consider a metric space, namely $\mathbb{R}^4$ with its usual metric."

 

[PeterDonis]

What I mean is, let the natural coordinates --just label of the points of $\mathbb{R}^2 \times \mathbb{S}^2$-- be $(t,r, \theta, \phi)$. Now, let's consider a metric space, namely $\mathbb{R}^4$ with its usual metric.

Why do you want to do this? It makes no sense.

Also, you still haven't understood: you need to understand the properties of a topological space without using any embedding of that space in another space.

I'm sorry, but I don't see the point of continuing to repeat the same advice and have a discussion if you continue to ignore that advice.

 

[PeterDonis]

The OP question in this thread has been answered, and the thread is closed. @davidge if you want to ask questions about the topological concept of a manifold with boundary, you can do that in the appropriate math forum; but please take the time to work through a textbook first.