Kantorovich spaces and the metrization problem (Q1335911)

The article grounds on the following simple idea. It is known that any \(K\)-space can be represented as the field of reals in a suitable Boolean-valued model (Gordon's theorem) [the author and \textit{S. S. Kutateladze}, `Nonstandard methods of analysis' (Russian) (1990; Zbl 0718.03046)]. Consequently, metrization by a \(K\)-space is nothing else but the usual metrization (i.e. that by means of the real numbers) in the corresponding Boolean-valued model. Successive implementation of this idea results in the notion of a Boolean algebra of fragments of uniformity which reflects the main structural peculiarity of the uniformities metrized.