For any ordered set P, the join dense completions of P form a complete lattice K(P) with least element O(P), the lattice of order ideals of P, and greatest element M(P), the Dedekind-MacNeille completion of P. The latticeK(P) is isomorphic to an ideal of the lattice of all closure operators on the lattice O(P). Thus it inherits some local structural properties which hold in the lattice of closu...

We introduce and study a subclass of meromorphic univalent functions with positive coefficients defined by novel operator obtain coefficient estimates, closure theorems, convolution properties, partial sums, δ- neighborhood for the class .

interpretation: Domains and surroundings. Abstract interpretation is a general theory for specifying and designing approximate semantics of program languages [10]. Approximation can be equivalently formulated either in terms of Galois connections or closure operators [11]. An upper closure operator ρ : C → C on a poset C (uco(C ) for short), representing concrete objects, is monotone, idempoten...

In this paper, notions of L-topological derived internal relation space, interior operator enclosed space and closure are introduced. It is proved that all these spaces categorically isomorphic to space.

In this paper we introduce the concept of Rees closure for subalgebras universal algebras. We denote by △

The Abiteboul and Beeri algebra for complex objects can express a query whose meaning is transitive closure, but the algorithm naturally associated to this query needs exponential space. We show that any other query in the algebra which expresses transitive closure needs exponential space, under a \call by value" evaluation strategy. This proves that in general the powerset is an intractable op...

We study the problem of listing all closed sets of a closure operator σ that is a partial function on the power set of some finite ground set E, i.e., σ : F → F with F ⊆ P(E). A very simple divide-and-conquer algorithm is analyzed that correctly solves this problem if and only if the domain of the closure operator is a strongly accessible set system. Strong accessibility is a strict relaxation ...