Some more algebra on ultrafilters in metric spaces

Abstract: We continue algebraization of the set of ultrafilters on a metric spaces initiated in [6]. In particular, we define and study metric counterparts of prime, strongly prime and right cancellable ultrafilters from the Stone-$\check{C}$ech compactification of a discrete group as a right topological semigroup [3]. Our approach is based on the concept of parallelity introduced in the context of balleans in [4].