Topics in Generalized Topology and Fuzzy Generalized Continuities This work is comprised of the generalized topology, algebraic generalized topology and fuzzy generalized topology. We have defined and studied the notions of semi- -local function, global function, global closure operator, global interior and -normal spaces in Ideal generalized topological spaces. Properties of these functions are investigated. Examples and counter examples are given where deemed necessary. We continued the investigations of some important results in generalized topological groups and proved basic properties of -connectedness. Along with other results, it is proved that in a -topological group, the maximal -connected components containing the identity of the group is -closed invariant subgroup. -quotients of -topological groups are also discussed. -topological vector spaces (generalization of TVS) are one of the interesting structures which is defined and investigated over here. This space is a blend of -topological structure with the algebraic concept of a vector space in such a way that vector addition and scalar multiplication are -continuous functions. A counter example is given to show that a -topological vector space is not a topological vector space. We have studied the concept of a fuzzy generalized topology which is a generalization of Chang’s fuzzy topology, and investigated some properties of its structure. We have also introduced the concept of fuzzy generalized open function and fuzzy generalized closed function in terms of fuzzy generalized interior and fuzzy generalized closure operators
المبحث الخامس: زواجها بعدما انتھت نازک الملائکۃ دراستھا في أمریکا عادت إلی بغداد وعینت أستاذۃ مساعدۃ في جامعتھا۔ فأصدرت عدۃ دواوین شعریۃ ونقدیۃ، وبعدہ فترۃ انتقلت من جامعۃ بغداد إلی جامعۃ البصرۃ، ثم تزوجت بالدکتور ’’عبدالھادي محبوبۃ في سنۃ 1962م۔ وزوجھا ھذا کان زمیلھا في جامعۃ بغداد في قسم اللغۃ العربیۃ في کلیۃ التربیۃ وکان عالماً لغویاً وأستاذاً سابقاً بجامعۃ الکویت، تزوجتہ نازک وھي تقرب الاربعین سنۃ من عمرھا۔ وعندما توفي زوجھا كانت ھي أیضاً مریضۃ وکانت مقیمۃ في القاھرۃ ولکنھا لا تعلم بوفاتہ المفاجئة، لأنھا کانت مریضۃ۔ لذلک لم یخبرھا أحد ولم یشأ أحداً نقل (النعي) إلیھا خوفًا من أن یضر بصحتھا، وبعد فترۃ من وفاتہ أخبروھا بأنّہ سافر إلی بغداد، وھي لا تعلم بأنھا الآن وحیدۃ وقد فارقھا رفیق حیاتھا، ویقول إبنھا البراق بأننا أخبرناھا بعد أسابیع من وفاتہ ودفنہ في القاھرۃ ورثتہ في قصیدۃ عنوانھا ’’أنا وحدي‘‘، ویبدو ھذہ آخر قصیدۃ قدمتھا نازک وتم نشرھا قبل وفاتھا۔
Islam is a divine religion. It is based on divine revelation and Sunnah of the Holy prophet (SAW). Tolerance, patience, forbearing and broadmindedness are the hallmarks of the last divine religion, Islam. In the article the ideology of co-existence has been discussed. Verses of the Holy book indicate importance of the tolerance. Similarly some events out of the Seerah of the Holy prophet (SAW) have been mentioned as references. In these pages it is impossible to explain scope of the subject; however efforts have been made to elaborate the Islamic perspective of tolerance. May Allah Almighty enable all of us to follow teachings of Islam in true spirit.
The purpose of present study was to identify dynamics of parenting in parent-child relationship, communication, self-esteem and academic achievements of female students. The core theme of current research addressed parent-child relationship by focusing on mother- daughter dyad. The main objective of research was to measure and compare parent-child relationship, parent-child communication, self-esteem and academic achievements between female students of public and private schools. From logical theoretical framework and rigorous synthesis of extensive review of relevant literature, all research variables & indicators were extracted, selected and identified for quantitative measurement. Four theoretical perspectives were analyzed to build theoretical framework, in which bio-ecological theory explained macro and micro environmental influences on child through coordination of different layers of family relations & systems of schools. Family system theory of communication explained family communication patterns& skill used by parent to enhance parent-child relationship in the family. Social capital theory addressed parent-child relationship as social capital for children to get academic achievement in their schools. Symbolic interactionism helped to explain the process of development of concept of self-esteem in adolescent girls. This theoretical framework provides philosophic reasoning and logic by connecting all facts together in a coherent whole. Quantitative survey design was used to get information through self- administrated questionnaire. It was a structured questionnaire that consisted on four parts including structured questions with probable key options given below. The participants of present study were female students of age ranged between 13 to 16 years from different public and private schools of Lahore, who were attending 8th and 9th classes respectively. The sample was consisting of 864 female students, in which 511 students were from public and 353 from private schools. Convenient sampling technique was used due to unequal distribution of population in the schools of public and private sectors. Data was statistically analyzed by applying Chi-square test to compare the frequencies between public and private schools. Results showed significant difference in almost all sets of variables of parent-child relationship and parent-child communication. However, the level of academic achievement was significantly higher in students of private schools as compared to public schools. Whereas, the level of self- esteem was significantly higher in both groups of female students from public & private school showing substantial self-worth of girls about themselves.