Please use this identifier to cite or link to this item:
http://hdl.handle.net/10603/339497
Title: | On Cubis Sets and Cubic Topological Spaces |
Researcher: | Loganayaki P |
Guide(s): | Jayanthi D |
Keywords: | Physical Sciences Mathematics Statistics and Probability |
University: | Avinashilingam Deemed University For Women |
Completed Date: | 2020 |
Abstract: | In this research work, various types of cubic sets are introduced and some results based on the newlineoperations of P-union, P-intersection, R-union and R-intersection are examined and counter examples newlineare given graphically. Also the concepts like interior, closure and various types of open and closed newlinesets, base, subbase, cubic point, continuous mappings, almost-continuous mappings and open mapping newlineare introduced in P-cubic topological spaces and R-cubic topological spaces. Also many properties and newlinecharacterizations of the newly defined open sets and continuous mappings are obtained. The concept newlineof connectedness is also studied in P-cubic topological spaces. newlinei) Major Objectives: newlineand#61623; To define various types of open sets on P-Cubic open topological spaces and compare the newlineinterrelations between them. newlineand#61623; To define various types of open sets on R-Cubic open topological spaces and compare the newlineinterrelations between them. newlineand#61623; To define various types of Continuous mappings and open mappings on P-Cubic open newlinetopological spaces and to study the interrelations between them. newlineand#61623; To define various types of Continuous mappings R-Cubic open topological spaces and to study newlinethe interrelations between them. newlineand#61623; To define various types of connectedness on P-Cubic open topological spaces and to study the newlineinterrelations between them. newlineii) Hypothesis newlineand#61656; To provide graphical representation for easy understanding. newlineand#61656; To provide examples for clear understanding of defined concepts. newlineiii) Methodology newlineand#61607; Theorems and Lemmas are proved for the interrelation between the defined sets. newlineand#61607; Examples are provided to show that the reverse implications are not true in general. newlineiv) Findings newlineand#61692; Also R-union and R-intersection the of two UIECS need not be UIECS. newlineand#61692; Also R-union and R-intersection the of two LIECS need not be LIECS. newlineand#61692; P-cubic regular open set is stronger than all other P-cubic open sets defined. newlineand#61692; R-cubic regular open set is stronger than all other P-cubic open sets defined. |
Pagination: | 130 p. |
URI: | http://hdl.handle.net/10603/339497 |
Appears in Departments: | Department of Mathematics |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
01_title.pdf | Attached File | 48.89 kB | Adobe PDF | View/Open |
02_certificate.pdf | 33.98 kB | Adobe PDF | View/Open | |
03_acknowledgement.pdf | 9.33 kB | Adobe PDF | View/Open | |
04_contents.pdf | 61.09 kB | Adobe PDF | View/Open | |
05_introduction.pdf | 207.37 kB | Adobe PDF | View/Open | |
06_review.pdf | 212.21 kB | Adobe PDF | View/Open | |
07_chapter1.pdf | 456.81 kB | Adobe PDF | View/Open | |
08_chapter 2.pdf | 275.39 kB | Adobe PDF | View/Open | |
09_chapter 3.pdf | 624.96 kB | Adobe PDF | View/Open | |
10_chapter 4.pdf | 483.54 kB | Adobe PDF | View/Open | |
11_chapter 5.pdf | 518.34 kB | Adobe PDF | View/Open | |
12_chapter 6.pdf | 422.7 kB | Adobe PDF | View/Open | |
13_summary and conclusion.pdf | 448.51 kB | Adobe PDF | View/Open | |
14_references.pdf | 240.38 kB | Adobe PDF | View/Open | |
80_recommendation.pdf | 270.8 kB | Adobe PDF | View/Open |
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