DOI: 10.15672/hujms.1797136 ISSN: 2651-477X

Hybrid Topologies on the Real Line II

Sami Lazaar, Tom Richmond, Khadhri Sabrine
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Given a subset $A \subseteq \mathbb{R}$, the Hattori topology $H(A)$ is a hybrid of the Euclidean and lower-limit topologies, giving every point $a \in A$ a base of Euclidean neighborhoods $(a-\ve, a+\ve)$ and every point $b \not\in A$ a base of lower-limit neighborhoods $[b, b+\ve)$. Here we consider hybrid topologies from the lower-limit and right-ray topologies on $\mathbb{R}$ as well as hybrid topologies formed from at least one Alexandroff topology on $\mathbb{R}$.

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