A new Lindelof topological group

TL;DR

This paper constructs a new Lindelof topological group using a subsemigroup generated by a specific L-space, expanding the known examples of such groups and raising questions about their finite powers.

Contribution

It introduces a novel example of a Lindelof topological group derived from a subsemigroup of a product of circles generated by J. Moore's L-space.

Findings

The subsemigroup generated by Moore's L-space is itself an L-space.

This construction yields a new example of a Lindelof topological group.

The Lindelof property of all finite powers of this group remains unresolved.

Abstract

We show that the subsemigroup of the product of w_1-many circles generated by the L-space constructed by J. Moore is again an L-space. This leads to a new example of a Lindelof topological group. The question whether all finite powers of this group are Lindelof remains open.