How are topological spaces used in physics?
Topology is relatively young and it develops rapidly. I'm not 100% sure whether topology as a whole or in parts has applications in physics, i.e. how "topological" these subjects really are:How are topological spaces used in physics?
Topology in its basics plays an important role in physics, simply because Hilbert spaces where physics mostly takes place are topological vector spaces.Quantitatively and conceptually, I know about as much as first year physics student physics-wise. Regarding topology, I hardly even know what it means.
Didn't convince me. A bit too simple and 3D for my taste, and partly wrong.
It would only locally be closed or open. Additionally, the EH is hardly a real life hyperspace.If it [EH] attaches to the exterior, then the known universe is topologically a closed set with respect to the black hole. If it [EH] attaches to the interior, then the known universe is topologically an open set.
Is that it? I would hardly call it work applying point set topology to black holes. All it says is that the outside of the EH is an open set, if you include the boundary it is a closed set. Same for the interior. That is trivial. Even the definition of a manifold to describe any spacetime (black hole or not) needs more topology than that.
Yes, but in this physical context "topology" means something else than the mathematical term.