Product of Chu spaces in the category of Chu(S-Act)

Abstract

The necessary conditions for the existence of products of Chu spaces in the category Chu(S-Act) over the category  of S-acts are obtained. It is proved the existence of a product of Chu spaces  $r_i: A_i\otimes X_i\longrightarrow D_i$ $(i\in I)$ in the category Chu (S-Act) in the cases of $X_i$ are zero polygons for any $i\in I$ or $D_i$ are zero polygons for any $i\in I$.