International
Tables for Crystallography Volume B Reciprocal space Edited by U. Shmueli © International Union of Crystallography 2010 
International Tables for Crystallography (2010). Vol. B, ch. 1.3, p. 29

It is defined by the family of seminormswhere K is now fixed. The fundamental system S of neighbourhoods of the origin in is given by sets of the formIt is equivalent to the countable subsystem of the , hence is metrizable.
Convergence in may thus be defined by means of sequences. A sequence in will be said to converge to 0 if for any given there exists such that whenever ; in other words, if the and all their derivatives converge to 0 uniformly in K.