[S] Super and Hyper Products of Super Relations
Árpád Száz, Szász Árpád (2024-) (xxx) · University of Debrecen Electronic Archive (University of Debrecen) · 2024
If R is a relation on X to Y, U is a relation on P (X) to Y, and V is a relation on P (X) to P (Y), then we say that R is an ordinary relation, U is a super relation, and V is a hyper relation on X to Y. Motivated by an ingenious idea of Emilia Przemska on a unified treatment of open-and closed-like sets, we shall introduce and investigate here four reasonable notions of product relations for super relations. In particular, for any two super relations U and V on X, we define two super relations U ∗ V and U ∗ V, and two hyper relations U ∗ V and U ∗ V on X such that (some text) By using the distributivity of the operation over, we can at once see that U ∗ V U ∗ V. Moreover, if U V, then we can also see that U ∗ V = U ∗ V. The most simple case is when U is an interior relation on X and V is the associated closure relation defined such that V (A) = U (Ac)c for all A X. © 2021 Mathematical Institute, Slovak Academy of Sciences.