This paper studies algebraic frames L and the set Min(L) of minimal prime elements of L. We will endow the set Min(L) with two well-known topologies, known as the Hullkernel (or Zariski) topology and the inverse topology, and discuss several properties of these two spaces. It will be shown that Min(L) endowed with the Hull-kernel topology is a zero-dimensional, Hausdorff space; whereas, Min(L) ...

If 〈L, <〉 is a dense linear ordering without end points and A and B disjoint dense subsets of L, then the topology OAB on the set L generated by closed intervals [a, b], where a ∈ A and b ∈ B, is finer than the standard topology, O<, generated by all open intervals and 〈L,OAB〉 is a GO-space. The basic properties of the topology OAB (separation axioms, cardinal functions, metrizability) are inve...

The Alexandrov–Fenchel inequality bounds from below the square of mixed volume V(K1,K2,K3,…,Kn) convex bodies K1,…,Kn in ℝn by product volumes V(K1,K1,K3,…,Kn) and V(K2,K2,K3,…,Kn). As a consequence, for integers α1,…,αm∈ℕ with α1+⋯+αm=n Vn(K1)α1n⋯Vn(Km)αmn suitable powers Vn(Ki) Ki, i=1,…,m, is lower bound V(K1[α1],…,Km[αm]), where αi multiplicity which Ki appears volume. It has been conjectur...

We continue the study of freezing sets for digital images introduced in [L. Boxer and P.C. Staecker, Fixed point topology, 1, Applied General Topology 2020; L. Boxer, 2, Convexity Freezing Sets Digital Topology, 2021]. prove methods obtaining $(X,c_i)$ $X \subset \mathbb{Z}^2$ $i \in \{1,2\}$. give examples to show how these can lead determination minimal sets.

We study strictly convex Alexandrov solutions u of the real MongeAmpère equation det(∇2u) = f , where f is measurable, positive, and bounded away from 0 and ∞. Under only these assumptions we prove interior Wregularity of u.

In this paper, we investigate the properties of Alexandrov fuzzy topologies and upper approximation operators induced by maps. We give their examples. AMS Subject Classification: 03E72, 03G10, 06A15, 06F07