A further remark: confusingly, the algebraic closure of Qp and its completion Cp are actually isomorphic as fields (and both are also isomorphic to C), since they are both algebraically closed fields of characteristic zero and of cardinality of the continuum.
A further remark: confusingly, the algebraic closure of Qp and its completion Cp are actually isomorphic as fields (and both are also isomorphic to C), since they are both algebraically closed fields of characteristic zero and of cardinality of the continuum.
Yup. Very different topologically, though.