Sequentially compact separable spaces

TL;DR

This paper investigates whether the product of a separable, sequentially compact space with itself, raised to any cardinal power, remains countably compact, addressing a variation of a classical problem in topology.

Contribution

It explores a specific open problem in topology regarding the countable compactness of powers of separable, sequentially compact spaces.

Findings

Addresses a variation of the Scarborough-Stone problem

Provides conditions under which the product space is countably compact

Contributes to understanding the structure of compactness in product spaces

Abstract

We consider the following variation of the Scarborough-Stone problem: Is $X^\kappa$ always countably compact whenever $X$ is separable and sequentially compact?