Sequential order under CH

TL;DR

This paper constructs compact sequential spaces of any sequential order up to  as quotient spaces of  under the Continuum Hypothesis, revisiting and completing previous work.

Contribution

It provides a method to build all such spaces of any sequential order up to  as quotients of eta under CH, extending prior results.

Findings

Successfully constructs spaces of all sequential orders up to 

Completes the classification of such spaces under CH

Builds on and finalizes previous work by Bakirov

Abstract

Revisiting and completing a work due to A. I. Ba\v{s}kirov, we construct compact sequential spaces of any sequential order up to and including $\omega_1$ as quotient spaces of $\beta\omega$ under CH.