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math.GN2024★ 4 cited
On the probabilistic metrizability of approach spaces
Hongliang Lai, Lili Shen, Junche Yu
We investigate approach spaces generated by probabilistic metric spaces with respect to a continuous t-norm on the unit interval . Let be the supremum of the idemp…
math.GN2021★ 2 cited
A Hofmann-Mislove theorem for approach spaces
Junche Yu, Dexue Zhang
The Hofmann-Mislove theorem says that the ordered set of open filters of the open-set lattice of a sober topological space is isomorphic to the ordered set of compact saturated set…
math.GN2021
Continuous [0,1]-lattices and injective [0,1]-approach spaces
Junche Yu, Dexue Zhang
In 1972, Dana Scott proved a fundamental result on the connection between order and topology which says that injective spaces are precisely continuous lattices endowed with S…