14273

12911

كارشناسي ارشد

رياضي محض (آناليز رياضي)

اصفهان : دانشگاه صنعتي اصفهان

1397

هفت، ۶۸ص.: مصور

فارسي به انگليسي

1397/11/06

كتابنامه

علوم رياضي

رياضي

1397/11/10

ID12911

Function lattices and compactifications Fatemeh Hosseinzadeh Fallah f hosein@math iut ac ir January 2016 Master of Science Thesis in Farsi Departement of Mathematical Sciences Isfahan University of Technology Isfahan 84156 8311 IranSupervisor Dr Mohammad Reza Koushesh koushesh@cc iut ac irAdvisor Dr Farid Bahrami fbahrami@cc iut ac ir2010 MSC Primary 46E05 54D80 54D35Keywords Function lattice F filter F ultrafilter Abstract Throughout the thesis let X be any non empty set We denote by F X the algebra of all real valuedmappings on X We denote by L X the subalgebra of F X consisting of all bounded elements ofF X For all f g F X the mappings f g X R and f g X R are defined by f g x max f x g x and f g x min f x g x for ever x X respectively By a function lattice on X we mean a vector subspace F of F X such that F contians the constant mappings and f g F and f g F for all f g F A filteron X is a non empty family of subsets of X with the following properies 1 If A B then A B 2 If A and A B X then B 3 A F family on X is a non empty family A of non empty subsets of X sush that for every A A withA X there exist some B A and a function f F such that f B 0 and f X A 1 An F filter on X is a filter on X which is also an F family on X Suppose that F is a lattice consisting of real valued mappings on a non empty set X which contains thecostant mappings We use certain filters on X determined by F to construct a compact Hausdorff spaceX such that bounded elements of F extendable continuously over X These extended mappings forma dense subspace of C X It is remarkable that we not need the Stone Weierstrass Theorem to provethe density of these extensions For a large part of the theory developed in this thesis it is the lattice structure of real valued mappingsthat is important for our development Therefore we work with a lattice of real valued mappings whichmight contain unbounded mappings The organization of thesis is as follows In chapter 1 after recalling some background and notations and definitions we discuss some basic prop erties of F filters that we shall need in establishing our main results

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