پديد آورنده :
ابراهيمي، صادق
عنوان :
نرم پذيري فضاهاي نرم دار احتمالي سر ستنف تعميم يافته
مقطع تحصيلي :
كارشناسي ارشد
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
يادداشت :
ص.ع.به فارسي و انگليسي
استاد راهنما :
محمدرضا كوشش
استاد مشاور :
فريد بهرامي
توصيفگر ها :
به طور توپولوژيك كران دار , موضعا محدب
تاريخ نمايه سازي :
10/4/93
استاد داور :
رسول نصر اصفهاني، مهدي نعمتي
چكيده انگليسي :
On the normability of generalized Serstnev PN spaces Sadegh Ebrahimi 2014 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Mohammad Reza Koushesh koushesh@cc iut ac ir Advisor Dr Farid Bahrami fbahrami@cc iut ac ir 2010 MSC 54E70 Keywords Probabilistic normed space Topologically bounded Locally convex Normability AbstractProbabilistic metric spaces have been rst de ned by Menger in 1942 Menger s idea was to replacethe distance d p q between two points p and q in a metric space X d by a distribution function Fpq The value of Fpq at x is then to be interpreted as the probability that the distance between p and q isless than x Menger s work was subsequent by Wald who modi ed Menger s idea In 1964 Serstnevgave the rst de nition of a probabilistic normed space The theory had little progress however sinceits introduction This motivated Alsina Schweizer and Sklar to rede ne probabilistic normed spacesin 1993 Their de nition included the previous de nitions as special cases In this thesis we adoptthe de nition of a probabilistic normed spaces as given by Alsina Schweizer and Sklar given in thefollowing Let denote the set of all distribution functions F such that F 0 0 The set isa metric space together with a standard metric called the Sibly metric By a probabilistic normedspace we mean a quadruple V v where V is a set v is a mapping from V to called theprobabilistic norm and and are triangle function such that Our purpose here is to studyconditions which guarantee a probabilistic normed space to be normable in the usual sense We willmake critical use of the Kolmogorov s theorem in normability of topological vector spaces A subsetA of a topological vector space X is topologically bounded if for every sequence an of real numberthat converges to 0 as n tends to and for every sequence pn of elements of A one has an pn in the topology of X According to Kolmogorov s theorem a T1 topological vector space is normable if and only if there is a neighborhood of the origin that is convex and topologically bounded Thisnaturally leads to study conditions under which a probabilistic normed space is a topological vector
استاد راهنما :
محمدرضا كوشش
استاد مشاور :
فريد بهرامي
استاد داور :
رسول نصر اصفهاني، مهدي نعمتي
