There is a theorem in linear algebra that if two vector space are of same finite dimension over the same field then they are isomorphic to each other. Now my question is that if two vector space are of same infinite dimension over the same field are they are isomorphic? If this result is true for infinite case then please suggest me how to prove it. If bases have same cardinality of two vectors spaces then there is one to one correspondence between their bases. But this one to one correspondence give results in finite cases. For infinite case i am stuck. Please suggest me. Thanks in advance.