A place of a number field is an isomorphism class of field maps onto a dense subfield of a nondiscrete locally compact field .
In the function field case, let be a function field of algebraic functions of one variable over a field. Then by a place in , we mean a subset of which is the ideal of nonunits of some valuation ring over .
of a number field 
is an isomorphism class of field maps 
onto a dense subfield of a nondiscrete locally compact field 
. 
be a function field of algebraic functions of one variable over a field 
. Then by a place in 
, we mean a subset 
of 
which is the ideal of nonunits of some valuation ring 
over 
.