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arXiv · 1805.01560

Separation axioms and covering dimension of asymmetric normed spaces

Victor Donjuán·Natalia Jonard-Pérez
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Abstract

In this paper, we approach the question if some of the separation axioms are equivalent in the class of asymmetric normed spaces. In particular, we make a remark on a known theorem which states that every $T_1$ asymmetric normed space with compact closed unit ball must be finite-dimensional. We also explore the product structure of these spaces and characterize the topological (covering) dimension of all finite-dimensional asymmetric normed spaces.

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Victor Donjuán, Natalia Jonard-Pérez. 2019-05-09. Separation axioms and covering dimension of asymmetric normed spaces. https://doi.org/10.2989/16073606.2019.1581298

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