Doctrine of Peace: An Islamic Perspective, an Analysis of the Hindrances in Peace Making Process

The present day global community is confronted with several challenges, absence of peace being the biggest one. The UNO and other regional organizations strive hard to achieve this goal. Unfortunately the world is far from achieving the goal of ensuring peace. It is also a fact that in most cases the Muslim world is in turmoil and it is involved or has been involved in one way or another. In order to find out the real causes of unrest, it is imperative to analyze the situation from academic, political, economic and social aspects.  This article deals with first aspect i.e. The academic. It has three parts, in the first part importance of peace has been elaborated in the light of the Quran and the Sunnah. In the second part, importance of peace treaties of the Prophet (PBUH), and one of His successors Umar, the second Caliph, has been brought in to focus. The issue that the foreign policy of Islamic State is based on perpetual peace has been discussed in this part. While in the third part those obstacles have been discussed which have caused to damage the  peace process in the world.

A Study of Some Aspects of Topologized Groups

A Study of Some Aspects of Topologized Groups A topological group is a mathematical object along with algebraic and topological structures. In this thesis our motivation is to study topological properties in the presence ofalgebraic structure particularly when the mappings are not continuous. It is a common question in topological algebra that how the relationship between topological properties depends upon the underlying algebraic structure. It is noticed that weaker the restriction in between algebraic structure and topology are, the larger is the class we obtain. Since we have weakened the condition of continuity and replaced it with the weaker form that is semi continuity and irresolute mapping and resultantly obtained s-(S-, Irresolute, Irr-) paratopologized or topologized groups. The purpose of this thesis is to give a mostly self contained study of s-(S-, Irresolute, Irr-) paratopologized or topologized groups. It is shown that every irresolute paratopological group is Irr-paratopological group as well as s-topological group. Every paratopological groups is s-paratopological group as well as S-paratopological group, and every Irr- paratopological group is S-paratopological group. Counter examples are given to show that such paratopological groups are generalized forms of the corresponding topologized groups. We have also defined and studied quasiboundedness of irresolute paratopological groups and s-paratopological groups. New notions- quasi bounded and - quasi bounded homomorphisms are introduced and discussed. In Chapter number six, we have defined semi-quotient mappings which are stronger than semi continuous mappings. Various interesting and important results on semi-quotients of paratopologized groups are proved. We have also studied semi connectedness for topologized groups.