Question

Converting a metric space to vector space

Answer 1

They are entirely different concepts. As to an origin, a general metric space does not have anything that behaves like the ordinary number zero does. A vector space does have a unique "zero-like" object, that is, a vector, that we often call 00, such that 0+v=v+0=v0+v=v+0=v for any vector vv in the space. Although the concepts of vector space and metric space are entirely different, some familiar spaces, uch as R3R3, are simultaneously vector spaces and metric spaces, and there is interaction between the vector structure and the metric structure.