Fuzzy Subgroups applied to Subgroups of the Group of Mbius Transformations

摘要

Let F be a family of subgroups of a group g = (G,) such that ∪F = G. Then P = (F,≤) is a partially ordered set (with an order dual to {is contained in}) and let a mapping A : G → P be a P-(fuzzy) subgroup of a group G defined by (6). The theory of fuzzy-subgroups is known [2] but in this paper we will apply it to the theory of Riemann surfaces. Mbius transformations form a group M and we introduce a connection between subgroups G {is contained in} M and the P-subgroups A : G → P. Finally, there are some examples which illustrates the situation.