Abstract
We obtain some quasi-metric properties of the dual cone of an asymmetric normed space. Thus, we prove that it is balanced, and hence its topology is completely regular. We also prove that it is complete in the sense of D. Doitchinov. These results generalize those obtained by Romaguera et al. in [18] because, in our study, the asymmetric normed space does not necessarily satisfy the \(T_1\) axiom. Moreover, we provide a class of asymmetric normed spaces whose dual cones are right K-sequentially complete. Finally, we represent an arbitrary asymmetric normed space as a function space by using the unit ball of its dual space.
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Alegre Gil, C. Quasi-Metric Properties of the Dual Cone of an Asymmetric Normed Space. Results Math 77, 178 (2022). https://doi.org/10.1007/s00025-022-01720-6
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DOI: https://doi.org/10.1007/s00025-022-01720-6