论文标题
在非架构的非架构模糊空间中严格的凸度的空隙
Voidness of strict convexity in non-Archimedean fuzzy normed spaces
论文作者
论文摘要
在简短的说明中，我们通过基本计算表明，非架构模糊范围（和2个字符）空间的概念无效。也就是说，根本没有严格的凸空间 - 甚至甚至是零维线性空间。 在此之前，我们还研究了严格凸出的非架构规范空间的情况。在这种情况下，我们看到满足此属性的唯一非零线性空间（在任意的非架构字段中定义）是$ \ mathbb {z}/3 \ mathbb {z} $上方的一维线性空间。 因此，像Mazur-Ulam定理一样，已证明这类空间的结果是微不足道或空的陈述。
In this short note, we show by elementary computations that the notion of non-Archimedean fuzzy normed (and 2-normed) spaces is void. Namely, there are no strictly convex spaces at all --not even the zero-dimensional linear space. Before this, we also study the case of strictly convex non-Archimedean normed spaces; in this setting we see that the only nonzero linear space (defined over an arbitrary non-Archimedean field) that satisfies this property is the one-dimensional linear space over $\mathbb{Z}/3\mathbb{Z}$. Consequently, the results that have been proven for this class of spaces, like the Mazur-Ulam Theorem, are either trivial or empty statements.
