论文标题
Menger关于角度空间解决两个旧问题的解决方案
A solution to two old problems by Menger concerning angle spaces
论文作者
论文摘要
1930年左右，K。Menger对抽象角度功能的概念表示了兴趣。他介绍了有关该概念的一般定义。他还提出了两个有关在欧几里得空间中具有角度函数的空间的共形嵌入性的问题。这些问题在后来的几年受到关注，但仅针对某些特定的度量空间。在本文中，我们首先更新角度函数的定义，以应用于具有相互作用概念的较大类别的空间，这在我们看来是一个更自然的框架。在这个新的一般环境中，我们解决了Menger提出的两个问题。
Around 1930, K. Menger expressed his interest in the concept of abstract angle function. He introduced a general definition of this notion for metric and semi-metric spaces. He also proposed two problems concerning conformal embeddability of spaces endowed with an angle function into Euclidean spaces. These problems received attention in later years but only for some particular cases of metric spaces. In this article we first update the definition of angle function to apply to the larger class of spaces with a notion of betweenness, which seem to us a more natural framework. In this new general setting, we solve the two problems proposed by Menger.
