Left-ray Right-ray Hybrid Topologies on the Real Line

Year 2024, Early Access, 1 - 12

Sami Lazaar , Tom Richmond , Khadhri Sabrine

https://doi.org/10.15672/hujms.1306300

Abstract

Given a nonempty set $A \subseteq \mathbb{R}$, we consider the smallest topology on $\mathbb{R}$ which contains the open left rays containing points $a \in A$ and the open right rays containing points $b \in \mathbb{R} - A$. We present a natural model for this hybrid topology and show that it is quasi-metrizable. We investigate other variations of this topology.

Keywords

hybrid topology, quasi-metric, Hattori topology

Supporting Institution

Brno University of Technology

Project Number

MeMoV II no. CZ.02.2.69/0.0/0.0/18-053/0016962.

Thanks

The second author acknowledges support from the Brno University of Technology (BUT) under the project MeMoV II no. CZ.02.2.69/0.0/0.0/18-053/0016962.

References

• [1] A. Bouziad and E. Sukhacheva, On Hattori spaces, Comment. Math. Univ. Carolin. 58 (2), 213–223, 2017