ON SOME SUBFIELDS OF K((X))

Let K be a commutative field and let K((X)) be the field of Laurent series in one variable X, consider with its natural X-adic topology. In this paper we prove that any closed subfield K subset of L subset of K((X)) is of the form L = K((f)) and K((X)) is algebraic over L of degree ordX(f). Some other properties of L are studied.