In this paper, we attempt to investigate the connection between various types of ideals (for examples $(m, n)$-ideal, bi-ideal, interior ideal, quasi ideal, prime ideal and maximal ideal) of an ordered semigroup $(S,cdot ,leq)$ and the correspond hyperideals of its EL-hyperstructure $(S,*)$ (if exists). Moreover, we construct the class of EL-$Gamma$-semihypergroup associated to a partially orde...

The aim of this paper is to introduce and study the notions of  (resp., pre, semi, )-open sets in terms of an ideal I. These concepts generalize the usual notions of  (resp., pre, semi, ) open sets. Also, several of their topological properties are investigated.

We explore ideal models for a programming language with recursive polymorphic types, variants of the model studied by MacQueen, Plotkin, and Sethi. The use of suitable ideals yields a close t between models and programming language. Two of our semantics of type expressions are faithful, in the sense that programs that behave identically in all contexts have exactly the same types.

When in 1867 botanists Carl Nageli and Simon Schwendener published their work on the microscope and its usage, they warned that using this optical device would never lead to a thorough comprehension of the observed the microscope could only present a corrupted picture of the object. Since the knowledge gained could never transcend the "received impression" of the beholder, there was "no truth f...