Rectangularity of products and completions of their subsets

The approach to the problem of the distribution of the functors of the Stone–Čech compactification, the Hewitt realcompactification or the Dieudonné completion with the operation of taking products is discussed using uniform structures on products. In particular, the role of different rectangular conditions is shown. Relative analogues of this question and new examples of (strongly) rectangular products are presented. Characterizations of bounded rectangular subsets of the product are given.