Abstract It is well known that every asymmetric normed space is a T0 paratopological group. Since all Ti axioms (i = 0, 1, 2, 3) are pairwise non-equivalent in the class of paratopological groups, it is natural to ask if some of these axioms are equivalent in the class of asymmetric normed spaces. In this paper, we will consider this question. We will also show some topological properties of asymmetric normed spaces that are closely related with the axioms T1 and T2 (among others). In particular, we will make a remark on [14, Theorem 13], which states that every T1 asymmetric normed space with compact closed unit ball must be finite-dimensional (as a vector space). We will show that when the asymmetric normed space is finite-dimensional, the topological structure and the covering dimension of the space can be described in terms of certain algebraic properties. In particular, we will characterize the covering dimension of every finite-dimensional asymmetric normed space.

中文翻译：

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非对称赋范空间的分离公理和覆盖维数

摘要 众所周知，每一个非对称赋范空间都是一个T0 并拓扑群。由于所有 Ti 公理 (i = 0, 1, 2, 3) 在副拓扑群类中都是成对非等价的，所以很自然地会问这些公理中的一些在非对称赋范空间类中是否等价。在本文中，我们将考虑这个问题。我们还将展示与公理 T1 和 T2（以及其他公理）密切相关的非对称赋范空间的一些拓扑特性。特别地，我们将对 [14, Theorem 13] 进行评论，其中指出每个具有紧闭单位球的 T1 非对称赋范空间必须是有限维的（作为向量空间）。我们将证明，当非对称赋范空间是有限维时，空间的拓扑结构和覆盖维数可以用某些代数性质来描述。特别地，我们将刻画每个有限维非对称赋范空间的覆盖维度。