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- Given a space in R_n = R_1 X R_2 X R_3 X R_4 ... can the metric for the R_1 x R_2 subspace be different from the metric for the R_3 X R_4 subspace?

I'm trying to get a handle on how general a space in R_n can be. Part of my motivation is the curled up dimensions physicists talk about. How does one dimension work differently than another dimension? Can one part of the dimensional structure follow one metric and another part follow a different metric?

I rather think it should be possible. That raises questions about the combinations of subspaces. Can R_1 X R_2 be different (say, taxicab geometry) from R_1 X R_3 (say, Euclidean) as long as R_1 X R_3 is consistent (um, somewhere in between maybe)?

Sorry if this is worded poorly, and if it's in an inappropriate folder. And how does one access the proper notation symbols?

Thanks.

I rather think it should be possible. That raises questions about the combinations of subspaces. Can R_1 X R_2 be different (say, taxicab geometry) from R_1 X R_3 (say, Euclidean) as long as R_1 X R_3 is consistent (um, somewhere in between maybe)?

Sorry if this is worded poorly, and if it's in an inappropriate folder. And how does one access the proper notation symbols?

Thanks.