Hybrid topologies on the real line

Given A ⊆ ℝ , the Hattori space H(A) is topological ( τA ) where each a ∈ has -neighborhood base { − ε + : > 0 } and b [ . Thus, may be viewed as hybrid of Euclidean topology lower-limit topology. We investigate properties spaces well other topologies on using various combinations discrete, left-ray, lower-limit, upper-limit, topologies. Since these generated by quasi-metric ℝ, we quasi-metrics which generate