Extensions of functions defined on products of pseudocompact spaces and continuity of the inverse in pseudocompact groups

It is proved that a Tychonoff pseudocompact group with continuous multiplication is a topological group. It is also proved that a Tychonoff countably compact group with separately continuous multiplication is a topological group. A continuous function defined on a product X × Y of pseudocompact spaces is extended to a separately continuous function defined on the product β(X) × β(Y) of their Stone-Сhech compactifications.