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 $(a-\ve, a+\ve)$ 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 $\mathbb{R}$.