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Abstract In this paper we show that, in contrast to what happens in a normed space, the weak topology of a finite dimensional asymmetric normed space is not necessarily the… Click to show full abstract
Abstract In this paper we show that, in contrast to what happens in a normed space, the weak topology of a finite dimensional asymmetric normed space is not necessarily the same as the topology of the asymmetric norm. We provide a class of finite dimensional asymmetric normed spaces where both topologies coincide. We also prove that the weak topology of an infinite dimensional asymmetric normed space is strictly coarser than the topology of the asymmetric norm.
Keywords:
finite dimensional;
weak topology;
asymmetric normed;
topology;
dimensional asymmetric
Journal Title: Topology and its Applications
Year Published: 2019
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Journal Title: Topology and its Applications
Year Published: 2019
Link to full text (if available)
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recommendations!