Please use this identifier to cite or link to this item:
https://ptsldigital.ukm.my/jspui/handle/123456789/499410| Title: | Generalization of confluent mappings theory in topological spaces |
| Authors: | Abdo Mohammed Ali Qahis (P52176) |
| Supervisor: | Mohd Salmi Md Noorani, Prof. Dr. |
| Keywords: | Mappings Continuum (Mathematics) |
| Issue Date: | 3-Dec-2013 |
| Description: | The present thesis explores some aspects of the generalization of the theory of confluent mappings via weak open sets. The study of confluent mapping and its properties was initiated by Charatonik in 1964. In this respect the variously modified forms of confluent mapping, by utilizing generalized continuum subsets, play a significant role in the field of continua theory in general topology. We started this research by recalling the history and the developments of this subject. Then, the objectives of the research were discussed and explained. Consequently, we presented the standard material on the continua theory, confluent mappings, connectedness, component, quasi-components, path-connectedness and path-component in the topological space, and some definitions and results that are needed for our thesis. The thesis is divided into four parts. In the first part, motivated by the idea of !-open sets, we introduced the notion of !-continuum subsets of topological space. By using this notion we presented new form of confluent mappings called !-confluent mappings. Then the notion of quasi-components were used to define the classes of quasi-confluent and quasi-!-confluent mappings, where the classes of confluent, !-confluent and quasi-confluent mappings are contained in the class of quasi-!-confluent mappings. We found all possible interrelations between these classes. Additionally, we have studied some operations on these mappings such as, composition property, composition factor property, factorization and the pullbacks. Furthermore, we generalize the notions of quasi-confluent and quasi-!-confluent mappings at some points of their ranges or relative to some points of their domains. In the second part of this study, we established weaker form of !-confluent mappings namely, semi-!-confluent, weakly !-confluent, !-joining mapping, and pseudo-!-confluent mappings. Some characterization and important properties of these mappings are discussed. In the third part of the research, we applied the concept of path-components in topological space to introduce stronger notions than the confluent and !-confluent mappings called path-confluent, path-!-confluent, strongly path-confluent, and strongly path-!-confluent mappings of which we have investigated all their fundamental properties. Moreover, several results about some operations on these mappings for example, the path-component restriction property, the component restriction property, composition property, and composition factor property were scrutinized. Some results on this part proved the relationship between these mappings and H-confluent mapping which was introduced by Joachim Grispolakis in 1978. In the fourth part of this research, we studied the localization and hereditary property of quasi-confluent and path-confluent mappings with regard to some of their operations. The approximative lifting property for induced mappings between metric hyperspaces were also dealt with.,Ph.D |
| Pages: | 131 |
| Call Number: | QA360.Q336 2013 |
| Publisher: | UKM, Bangi |
| Appears in Collections: | Faculty of Science and Technology / Fakulti Sains dan Teknologi |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| ukmvital_71625+Source01+Source010.PDF Restricted Access | 545.14 kB | Adobe PDF |  View/Open |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.