Functions on products of pseudocompact spaces

TL;DR

This paper proves that continuous functions on finite products of pseudocompact spaces can be extended to separately continuous functions on their Stone-Cech compactifications, generalizing the understanding of function extension in topology.

Contribution

It establishes a new extension property for continuous functions on products of pseudocompact spaces to their Stone-Cech compactifications.

Findings

Continuous functions extend to separately continuous functions on compactifications.

Extension holds for finite products of pseudocompact spaces.

Generalizes previous results on function extension in topology.

Abstract

For every natural number $ n $, any continuous function on the product of $ X_1 \times X_2 \times ... \times X_n $ pseudocompact spaces extends to a separately continuous function on the product $ \beta X_1 \times \beta X_2 \times ... \times \beta X_n $ of their Stone-Cech compactifications.