The Theory Of Algebraic Semi Rings - 2275 Words

ON BORNOLOGICAL SEMI RINGS ANWAR N. IMRAN Abstract. Our main focus in this work is to generalizes the theory of algebraic semi ring from the algebraic setting to the framework of bornological set. More specifically, the concept of new structure bornological semi ring BSR is introduced and the fundamental constructions in the class of bornological semi rings are discussed. In particular, the existence of arbitrary projective limits and arbitrary inductive limits of bornological semi ring is ensured. Additionally, the description of the category of bornological semi rings is presented and we study the product, coproduct and fiber product. Key words: Bornological Set, Bornological Ring. 1. Introduction The notion of a bounded subset of (real or complex) topological vector space was introduces by von Neamann. That motivated the definition and more general classes bounded sets and called bornologies. A bornological space is a type of space in functional analysis and it is very useful to solve problem of boundedness for set of elements and functions. That means, the main goal for bornology is to determine the boundedness, location and sitting the boundary for any area. A bornology on a set X is a family ÃŽ ² of subsets of X, such that; †¢ Every singleton set fxg is in ÃŽ ², that means, ÃŽ ² covering X ; †¢ If A ⊂ B, B 2 ÃŽ ² then A 2 ÃŽ ²; †¢ ÃŽ ² is stable under finite union. The elements of ÃŽ ² are called bounded subsets of X. Let X and Y be two bornological sets, a map f : X ! Y is called bounded ifShow MoreRelatedMathopoly Bagatelle an Alternative Instructional Tool in Teaching Mathematics4732 Words   |  19 Pagesof the game revolves on the triangle. A triangle is formed with the points and the origin. The player must then identify the triangle that is formed before determining the length of the sides of the triangle by simply looking at the board. This, in theory, decreases the time it takes for students to solve for the sides and slopes of the triangle. This is also able to increase comprehension of the student regarding a subject matter. This study is formulated to create a Mathematical Intervention MaterialRead MorePhysics in Daily Life13985 Words   |  56 Pagesused in Physics; consistently apply Physics principles in everyday situations; show a very good understanding of the development of principles by key scientists within a historical context; demonstrate a very good understanding of how scientific theories can be changed by new evidence and identify areas of uncertainity in Physics. recall and show understanding of a range of scientific facts, principles, concepts and practical techniques across parts of the Physics syllabus; use the correct scientificRead MoreStrategic Marketing Management337596 Words   |  1351 Pagesnecessarily is or is not ‘marketing’. They go on to suggest that the AMA definition presents marketing as a functional process conducted by the organization’s marketing department, whereas the general thrust of the more recent literature on marketing theory is that market ing is increasingly being conceptualized as an organizational philosophy or ‘an approach to doing † 4 S T R AT E G I C M A R K E T I N G M A N A G E M E N T business’. This strategic as opposed to a functional approach to