For simplicity, we adopt the following rules: i, x, I denote sets, A, M denote many sorted sets indexed by I, f denotes a function, and F denotes a many sorted function indexed by I. The scheme MSSUBSET deals with a set A , a non-empty many sorted set B indexed by A , a many sorted set C indexed by A , and a unary predicate P , and states that: If for every many sorted set X indexed by A holds ...

Relativizing an idea from multiplicity theory, we say that an element x of a von Neumann algebra M is n-divisible if W (x) ∩ M unitally contains a factor of type In. We decide the density of the n-divisible operators, for various n, M, and operator topologies. The most sensitive case is σ-strong density in II1 factors, which is closely related to the McDuff property. We make use of Voiculescu’s...

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 △