Group hyperreals: iterated sequential completions of rationals

Rok, strany: 1995, 89 - 96

We construct sequential convergence group completions of the rational numbers the underlying groups of which differ from the real numbers. First, we equip the group of real numbers with an incomplete compatible sequential convergence which preserves the usual metric convergence of rational sequences. Second, every completion of the resulting group has the desired properties. We show that there are exactly $\exp\expω$ such nonhomeomorphic completions; the sequential order of each completion is at least 2 and there are $\exp\expω$ completions the sequential order of which is $ω₁$.

ISO 690:

Frič, R. 1995. Group hyperreals: iterated sequential completions of rationals. In Tatra Mountains Mathematical Publications, vol. 5, no.1, pp. 89-96. 1210-3195.

APA:

Frič, R. (1995). Group hyperreals: iterated sequential completions of rationals. Tatra Mountains Mathematical Publications, 5(1), 89-96. 1210-3195.