Prüfer Ring

A metric space $\hat{\Bbb{Z}}$ in which the closure of a congruence class $B(j,m)$ is the corresponding congruence class $\{x \in\hat{\Bbb{Z}}\vert x\equiv j\ \left({{\rm mod\ } {m}}\right)\}$.

References

Fried, M. D. and Jarden, M. Field Arithmetic. New York: Springer-Verlag, pp. 7-11, 1986.

Postnikov, A. G. Introduction to Analytic Number Theory. Providence, RI: Amer. Math. Soc., 1988.