PRODUCTS OF LOCALLY PSEUDOCOMPACT TOPOLOGICAL-GROUPS

An old theorem of Comfort and Ross to the effect that the product of any number of pseudocompact groups remains pseudocompact is generalized, and a brief survey of some known results of locally pseudocompact groups is given. The product of any number of pseudocompact regularly closed subspaces of topological groups is proved to be pseudocompact. A corollary is obtained that the classes of locally pseudocompact groups and of locally compact groups behave similarly with respect to products. Additional known facts concerning products of functionally bounded sets that are connected with the results are briefly surveyed.