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

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01_title.pdfAttached File48.89 kBAdobe PDFView/Open
02_certificate.pdf33.98 kBAdobe PDFView/Open
03_acknowledgement.pdf9.33 kBAdobe PDFView/Open
04_contents.pdf61.09 kBAdobe PDFView/Open
05_introduction.pdf207.37 kBAdobe PDFView/Open
06_review.pdf212.21 kBAdobe PDFView/Open
07_chapter1.pdf456.81 kBAdobe PDFView/Open
08_chapter 2.pdf275.39 kBAdobe PDFView/Open
09_chapter 3.pdf624.96 kBAdobe PDFView/Open
10_chapter 4.pdf483.54 kBAdobe PDFView/Open
11_chapter 5.pdf518.34 kBAdobe PDFView/Open
12_chapter 6.pdf422.7 kBAdobe PDFView/Open
13_summary and conclusion.pdf448.51 kBAdobe PDFView/Open
14_references.pdf240.38 kBAdobe PDFView/Open
80_recommendation.pdf270.8 kBAdobe PDFView/Open


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