Let us note that a g -compatible Riemannian metric g R in a triple ( g , g R , h 0 ) defines a g -compatible distance function on a world manifold X . Such a function brings X into a metric space whose locally Euclidean topology is equivalent to a manifold topology on X . Given a gravitational field g , the g -compatible Riemannian metrics and the corresponding distance functions are different for different spatial distributions F and F ′ . It follows that physical observers associated with these different spatial distributions perceive a world manifold X as different Riemannian spaces. The well-known relativistic changes of sizes of moving bodies exemplify this phenomenon.