具有不传递等价关系的几何
Geometries with intransitive equivalence relation
摘要：
人们用不传递等价关系来考虑几何。这样的几何是物理几何，即它完全由世界函数描述，世界函数是平方距离函数的一半。物理几何一般不能公理化。它是由于变形的正常欧几里德几何。物理几何类比公理化几何类更强大。物理几何允许人们描述诸如离散性、粒度和有限可除性等几何性质。这些性质在应用于时空时是很重要的。他们承认一个解释歧视性质的时空，产生离散参数的基本粒子。物理几何的数学形式非常简单。物理几何是用几何术语（点和世界函数）来表述的，而不使用描述手段（坐标系、空间维度、流形等）。
英文摘要：
One considers geometry with the intransitive equaivalence relation. Such a geometry is a physical geometry, i.e. it is described completely by the world function, which is a half of the squared distance function. The physical geometry cannot be axiomatized, in general. It is obtained as a result of deformation of the proper Euclidean geometry. Class of physical geometries is more powerful, than the class of axiomatized geometries. The physical geometry admits one to describe such geometric properties as discreteness, granularity and limited divisibility. These properties are important in application to the space-time. They admits one to explain the discrimination properties of the space-time, which generate discrete parameters of elementary particles. Mathematical formalism of a physical geometry is very simple. The physical geometry is formulated in geometrical terms (in terms of points and world function) without a use of means of description (coordinate system, space dimension, manifold, etc.).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
