On the Characterizations of Approach Groups
In this paper, we present several characterizations on approach groups, and ultra-approach groups. In doing so, we first give necessary and sufficient conditions for an approach structure to be compatible with group structure. We show that every ultra-approach group is ultra uniformizable. Secondly, starting with an approach space, and its natural neighborhood system on a group, we characterize the resulting neighborhood approach group. Finally, we show that the category of ultra-approach-Cauchy group is a topological category, and more importantly, we show that the category of ultra-approach groups an the category of strongly limit groups are isomorphic.
In this paper, we present several characterizations on approach groups, and ultra-approach groups. In doing so, we first give necessary and sufficient conditions for an approach structure to be…
Introducing the notion of probabilistic convergence ring, and probabilistic limit ring, our motivations among others are, to focus at two vital issues, such as, (a) to provide characterization…
Starting with the category of probabilistic approach groups, we show that the category of approach groups can be embedded into the category of probabilistic approach groups as a bicoreflective…