Left-ray right-ray hybrid topologies on the real line

Abstract

Given a non-empty 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.

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