Question

vector space and metric space both are spaces. is there any relation between them?

Answer 1

vector space is a space that is complient with well known axioms. A metric space is a vector space with distance defined on it.

Answer 2

means in a metric space when we take a set say X then X must be vector space?

Answer 3

A vector space is more general, a metric space has an additional specification that gives a "size" measurement.

Answer 4

it depends on your X choice. It will have to include the 0 vector to be a subspace of a vector space

Answer 5

please explain ''It will have to include the 0 vector to be a subspace of a vector space'' if you can.

Answer 6

means X is vector space or subspace of a vector space then why u specify 0 vector?