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On a smooth manifold tangent bundle can be thought of as a space of its sections, i.e. vector fields. Usually they supposed to be smooth or continuous, but, more generally, one can consider measurable sections (vector fields consisted of vectors, measurably dependent on the point of manifold). One can also equip this space of measurable vector fields with ...


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I post here the answer I received for the same question in mathoverflow: Here I list some facts that may be useful for building your intuition: 1. Two commutative Morita equivalent $C^*$-algebra are in fact $*$-isomorphic. 2 If $A$ is $C^*$-algebra and you take $B=M_n(A)$ then $A$ and $B$ are Morita equivalent. 3 Many invariants for $C^*$-algebras such as ...



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