  In this work, we examine one two-parameter family of sets consisting of
functions holomorphic in the unit disk, previously investigated by several
mathematicians. We focus on the set-theoretic properties of this family,
identify the general form of filtrations within it, and discover that it is not
a lattice. This insight motivates us to introduce a refined concept of
quasi-infima and quasi-suprema, and to establish their complete description.
  Unexpectedly, some new properties of the Gau\ss\ hypergeometric function play
a crucial role in our investigation.
