Theoretical study investigates hybrid topologies combining lower-limit, right-ray, and Alexandroff spaces on the real line, expanding generalized topological space classifications.
Given a subset A ⊆ R, the Hattori topology $H(A)$ is a hybrid of the Euclidean and lower-limit topologies, giving every point a ∈ A a base of Euclidean neighborhoods (a-, a+) and every point b ∈ A a base of lower-limit neighborhoods [b, b+). Here we consider hybrid topologies from the lower-limit and right-ray topologies on R as well as hybrid topologies formed from at least one Alexandroff topology on R.
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Lazaar et al. (2026) studied this question.