 Each element of the dyadic solenoid corresponds to a character of the "p"-adic rationals that maps "a"/p"b" to the complex number "q""b""a".Conversely, every character "χ" of the "p"-adic rationals corresponds to the element of the "p"-adic solenoid given by "q""i" = "χ"(1/p"i").As a topological space the "p"-adic solenoid is a solenoid, and an indecomposable continuum.