标题： 拓扑锥和正极化双曲范数 显示英文标题

标题： Topological cones and positively polarizable hyperbolic norms

摘要： 在本文的第一部分，我们研究全序域上的线性锥体。我们证明，对于每个这样的锥体，唯一地存在一个泛向量空间（称为其张成的向量空间），它作为生成的凸锥嵌入其中。此外，我们研究了使自然锥体运算连续的锥体拓扑，并研究了这些拓扑如何传递到张成的向量空间。在第二部分中，我们处理满足极化恒等式且定义在实数锥体上的双曲范数。我们证明，在合理的假设下，这样的双曲范数在张成的向量空间上诱导出一个洛伦兹内积。最后，我们建立了在洛伦兹内积的威克旋转下的完备性与序理论完备性之间的联系。 显示英文摘要

摘要： In the first part of this article, we study linear cones over totally ordered fields. We show that for each such cone there uniquely exists a universal vector space (called its spanned vector space) into which it embeds as a generating convex cone. Moreover, we investigate topologies on cones for which the natural cone operations are continuous, and study how these topologies carry over to the spanned vector space. In the second part, we deal with hyperbolic norms which satisfy a polarization identity and are defined on cones over the real numbers. We show that, under reasonable assumptions, such hyperbolic norms induce a Lorentzian inner product on the spanned vector space. Finally, we establish a link between completeness under the Wick rotation of a Lorentzian inner product and order-theoretic completeness.