Topologies on groups determined by sequences: Answers to several questions of I.Protasov and E.Zelenyuk

TL;DR

This paper investigates topologies on groups defined by T-sequences, addressing open questions and analyzing the supremum operation of two such topologies, thereby advancing understanding in the structure of group topologies.

Contribution

It provides answers to specific open questions about T-sequence determined topologies and explores the properties of their supremum operation.

Findings

Resolved several open questions posed by Protasov and Zelenyuk.

Analyzed the behavior of the supremum of two T-sequence determined topologies.

Enhanced understanding of the structure and properties of these topologies.

Abstract

We answer several questions of I.Protasov and E.Zelenyuk concerning topologies on groups determined by T-sequences. A special attention is paid to studying the operation of supremum of two group topologies.