The aim of this paper is to establish a fuzzy version of the dualitybetween domains and completely distributive lattices. All values aretaken in a fixed frame $L$. A definition of (strongly) completelydistributive $L$-ordered sets is introduced. The main result inthis paper is that the category of fuzzy domains is dually equivalentto the category of strongly completely distributive $L$-ordereds...

Let L be a real (Hausdorff) topological vector space. The space %[L] of nonempty compact subsets of L forms a (Hausdorff) topological semivector space with singleton origin when 3C[L] is given the uniform (equivalently, the finite) hyperspace topology determined by L. Then %[L] is locally compact iff L is so. Furthermore, 90.[Z,], the set of nonempty compact convex subsets of L, is the largest ...

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...

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.

An L-embedded Banach spaace is a Banach space which is complemented in its bidual such that the norm is additive between the two complementary parts. On such spaces we define a topology, called an abstract measure topology, which by known results coincides with the usual measure topology on preduals of finite von Neumann algebras (like L 1 ([0, 1])). Though not numerous, the known properties of...

In this paper, we investigate two L-neighborhood systems induced by an Lfuzzy topology in a complete residuated lattice L. We study the relationships among L-fuzzy topology, L-topologies and L-neighborhood systems. Finally, we give their examples. AMS Subject Classification: 03E72, 06A15, 06F07, 54A05

It is well known that lattice-valued rough sets are important branches of fuzzy sets. The axiomatic characterization and related topology the main research directions For L=(L,⊛), a complete co-residuated lattice (CCRL), Qiao recently defined an L-fuzzy lower approximation operator (LFLAO) on basis relation. In this article, we give further study Qiao’s LFLAO around induced L-topology. Firstly,...

In the present paper we study the smooth topology and its equivalentL-topology, the corresponding L-continuous, L-open, and homeomorphism maps.We also study the concept of several separation axioms (like ST◦, ST1, ST2, andtheir strong and weak forms on the mentioned topology). Finally we investigatesome of their properties and the relations between them.MSC 2010. 39B72, 47H0...