Hybrid topologies on the real line II

Abstract

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 $(a-\varepsilon, a+\varepsilon)$ and  every point $b \not\in A$ a base of lower-limit neighborhoods $[b, b+\varepsilon)$.   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 $\mathbb{R}$.

Keywords

• hybrid topology
• Hattori topology
• lower-limit topology
• right ray topology
• Alexandroff topology

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