The pure rotational spectrum of a minor isotopologue of ytterbium fluoride, 171YbF, in the X2Σ+ (v=0) state has been recorded using Fourier transform microwave (FTMW) spectroscopy and pump/probe microwave optical double resonance (PPMODR) spectroscopy. The pure rotational spectra and precisely measured splittings in the (0,0) A2Π1/2←X2Σ+ band were analyzed to produce an improved set of fine and magnetic hyperfine parameters for the X2Σ+ (v=0) state of 171YbF. A comparison with theoretical predictions is made.

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 ultrahomogeneous – 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 (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.