The Tensor product of ƒ-algebras

Abstract

In this paper we prove that the Fremlin tensor product of two ƒ-algebras can be endowed with an ƒ-algebra structure and satises an appropriate universal property. In particular, the Riesz tensor product C(X)⊗̄C(Y ) of C(X) and C(Y ), where X and Y are topological spaces, is an ƒ-subalgebra of C(X x Y ).

Mathematics Subject Classication (2010): 46A40, 46H05, 06F25.

Key words: Tensor product, ƒ-algebras, Riesz subspace.