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Title: A Study on g b Closed Sets in Topological Bitopological and Tritopological Spaces
Researcher: Priyadharsini P
Guide(s): Parvathi A
Keywords: Topology
University: Avinashilingam Deemed University For Women
Completed Date: 19.01.2016
Abstract: In the field of Mathematics topology plays a vital role. Topology has shown its fruitfulness in both pure and applied domains. In the field of real life, topological structures on the collection of data are suitable mathematical models for mathematizing not only the quantitative data but also the qualitative data. The influence of topological spaces can be observed in the fields like computer science, digital topology and computational topology for geometric and molecular design, data mining, information systems, quantum physics, particle physics, high energy physics and superstring theory. newlineClosed sets are fundamental objects in topological spaces. In the study of topological spaces many concepts of topology have been generalized by introducing the concept of semi open sets (Levine (1963)) instead of open sets. Andrijevic (1996) introduced the notion of b - open sets as a generalization of open sets in topological spaces. Levine (1970) introduced the concept of generalized closed (briefly, g - closed) sets in topological spaces. Using this concept and Levine s idea many researchers have introduced and studied various types of generalized closed sets. The concept of w - closed sets was introduced by Hdeib (1982). Arya et al. (1990) introduced generalized semi closed (briefly, gs - closed) sets in topological spaces. Veerakumar (2000) introduced generalized star closed (briefly, g* - closed) sets in topological spaces. Vidhya et al. (2012) introduced a new class of sets called generalized star b - closed (briefly, g*b - closed) sets which is between the class of b - closed and the class of gb - closed sets. newlineThe notion of continuous maps is one of the most important concepts in topological spaces. Kempisty (1932), Levine (1960), Jain (1980), Dontchev (1996) and Kohil et al. (2008) introduced quasi continuous maps, strongly continuous maps, totally continuous maps, contra continuous maps and perfectly continuous maps respectively.
Pagination: 186 p.
Appears in Departments:Department of Mathematics

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04_content.pdf42.52 kBAdobe PDFView/Open
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06_chapter-2.pdf442.88 kBAdobe PDFView/Open
07_chapter-3.pdf564.27 kBAdobe PDFView/Open
08_chapter-4.pdf363.96 kBAdobe PDFView/Open
09_chapter-5.pdf300.94 kBAdobe PDFView/Open
10_chapter-6.pdf324.62 kBAdobe PDFView/Open
11_chapter-7.pdf213.52 kBAdobe PDFView/Open
12_chapter-8.pdf138.58 kBAdobe PDFView/Open
13_chapter-9.pdf259.52 kBAdobe PDFView/Open
14_summary.pdf23.08 kBAdobe PDFView/Open
15_biobliography.pdf105.43 kBAdobe PDFView/Open

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