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x[itex]\cdot[/itex]y = -x[itex]^{0}[/itex]y[itex]^{0}[/itex]+x[itex]^{i}[/itex]y[itex]^{i}[/itex]

for the definition of coninuity; it is a misinformer about the proximity of points. Should I use the Euclidean metric instead?

Thank's...

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- Thread starter cosmic dust
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- #1

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x[itex]\cdot[/itex]y = -x[itex]^{0}[/itex]y[itex]^{0}[/itex]+x[itex]^{i}[/itex]y[itex]^{i}[/itex]

for the definition of coninuity; it is a misinformer about the proximity of points. Should I use the Euclidean metric instead?

Thank's...

- #2

WannabeNewton

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Right?

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http://en.wikipedia.org/wiki/Spacetime_topology

(see Alexandrov [interval] topology)

- #5

WannabeNewton

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I've never seen pseudo-Riemannian metric tensors on vector spaces being used to induce a topology on the vector space but that's not to say that it isn't defined (you can define it in the same way). The canonical topology on Minkowski space-time would just be that generated by the base of open balls of the Euclidean metric yes. There are other topologies you can endow as well of course and they don't have to stem from a metric.I took the wikipedia's definition of Minkowski space: a 4-D real vector space with a symmetric, bilinear, non-degenerate quadratic form with signature (1,3). From this point of view, can a consistent metric induced by that quadratic form? If not, then according to your comment, I will have to make use and of the Eucliden norm on that vector space, in order to define continuity.

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