RESEARCH ARTICLE

Some more algebra on ultrafilters in metric spaces

Igor  Protasov

Faculty of Computer Science and Cybernetics, Kyiv University, Academic Glushkov pr. 4d, 03680 Kyiv, Ukraine

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-Čech 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].

Keywords: metric space, ultrafilter, ball invariance, parallelity, prime and strongly prime ultrafilters.

MSC: 22A15, 54D35, 54E15

Received: 14.02.2018

Language: English