/sci/ - Science & Math

>>11225577
Tensors as in smooth sections of [math]TM^n \otimes TM*^m[/math]?
Yeah, pretty sure. Diffeomorphism to R^n, pull back local trivialization of the tensor bundle, define the action by multiplication on the basis. Trivially independent of chart, should preserve smoothness.
>>11225657
There are spaces of real non-integer Hausdorff dimension, i.e. https://en.wikipedia.org/wiki/Hausdorff_dimension , but I'm not sure there're ones considered to be R^a.
>>11225682
He's talking about infinite-dimensional vector spaces.
>>11225749
When N is the cardinality of a large set.
>>11226200
https://en.wikipedia.org/wiki/Tryon%27s_Rat_Experiment
>>11226428
Khan Academy.