From Urysohn's Universal Metric Space to a Universal Space-Time

Authors

A. G. Aksoy, Claremont McKenna CollegeFollow
Z. Glassman, Pomona CollegeFollow
Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

10-2013

Comments

Technical Report: UTEP-CS-13-63

Published in Mathematical Structures and Modeling, 2013, Vol. 28, No. 2, pp. 28-34.

Abstract

A known Urysohn's result shows that there exists a universal} metric space, i.e., a metric space into every other (separable) metric space can be isomorphically embedded. Moreover, this universal metric space can be selected to be ultra-homogeneous -- every isomorphism of its two finite subsets can be extended to the isomorphism of the whole space.

Starting with Einstein's theories of Special and General relativity, space-times are described by a different type of structure -- a set (of events) equipped with the proper time t(a,b) between points a and b; such spaces are known as space-times with kinematic metric, or k-space-times. In this paper, we show that Urysohn's result can be extended to k-space-times -- namely, that there exists an ultra-homogeneous universal k-space-time.