The exponential growth of data generates terabytes of very large databases. The growing number of data dimensions and data objects presents tremendous challenges for effective data analysis and data exploration methods and tools. Thus, it becomes crucial to have methods able to construct a condensed description of the properties and structure of data, as well as visualization tools capable of r...

A topological translation plane may be defined as a system L of a‰ne l-dimensional subspaces of R such that (1) any two points are joined by a unique line L A L and joining is continuous; (2) Euclid’s parallel postulate holds and L is invariant under translation. It is easy to see that one of the two parts of condition (2) may be omitted. We use topological methods to show that (2) may be omitt...

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 study aimed to evaluate the effects of using Artemia franciscana enriched with cod liver oil and vitamins C and E on the growth, survival and stress resistance of juvenile Sepia pharaonis (Pharaoh cuttlefish). Twenty-five days after hatching, the larvae of S. pharaonis were transferred into culture tanks with an average length of 15.97±0.15 mm and average body weight of 3.53±0.03 g, in ele...

Here, we define (semi)topological L-algebras and some related results are approved. Then deduce conditions that mention an L-algebra to be a semi-topological or topological check attributes of them. Chiefly, display in L, if (L, ↠, τ ) is {1} open set L bounded satisfies the double negation property, then (L,τ) L-algebra. Finally, construct discrete topology on quotient L-algebra, under suit- a...

With L a complete lattice and M a continuous lattice, this paper demonstrates an adjunction between M-valued L-topological spaces (i.e. (L,M)-topological spaces) and Idl(M)-valued L-topological spaces where Idl(M) is the complete lattice of all ideals of M. It is shown that the right adjoint functor provides a procedure of generating (L,M)-topologies from antitone families of (L,M)-topologies. ...

Modern axiomatics of elementary geometry has steadily followed Hubert's program of elimination of continuity arguments. A brilliant example of the success of this method is to be found in the book [l ] by F. Bachmann which gives a unified treatment for geometries over arbitrary fields of characteristic y¿2. On the other hand the author has shown [2 ] that the plane axioms of incidence and order...

I discuss a topological relation of the conduction property of a many-particle system on a periodic lattice at zero temperature to the energy spectrum. When the particle number per unit cell is an irreducible fraction p/q, an insulator must have q low-lying states of energy O(1/L) in one dimension and of energy O(1) in two dimensions, where L is the linear system size.