Free PDF Multiset Relations and Topologies on Multisets, by K. P. Girish, Sunil Jacob John
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Multiset Relations and Topologies on Multisets, by K. P. Girish, Sunil Jacob John
Free PDF Multiset Relations and Topologies on Multisets, by K. P. Girish, Sunil Jacob John
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Multiset is a collection of objects in which the elements are allowed to repeat. The notion of multiset relations and multiset functions are introduced and the concepts in general topology on classical sets are extended to topology on multisets. Partially ordered multisets and their chains and antichains are introduced and the decomposition theorem for partially ordered multisets is obtained. Moreover multiset topologies are generated using multiset relations and to obtain a quasi-discrete multiset topology from a symmetric multiset relation instead of an equivalence multiset relation. Rough multisets are introduced and the relationship between rough multisets and multiset topologies are investigated.
- Sales Rank: #10564004 in Books
- Published on: 2012-12-03
- Released on: 2012-12-03
- Original language: English
- Number of items: 1
- Dimensions: 8.66" h x .28" w x 5.91" l, .41 pounds
- Binding: Paperback
- 120 pages
About the Author
Dr.Girish K P, Asst. Prof., Center for Cyber Security, Amrita Vishwa Vidyapeetham University, India. His areas of research interest are Multiset Theory and Cryptography.Dr Sunil Jacob John, Associate Prof., Dept. of Mathematics, NIT Calicut, India. His areas of research interest are Fuzzy Mathematics, Topology, Multiset and Dimension Theory.
Most helpful customer reviews
0 of 0 people found the following review helpful.
I am really enjoying this book.
By Moon Ho Hwang
I have been getting into the world of multi-set (shortly mset), and found this book (with another book "A Study of Multiset Algebra..." too.) This book seems like a Ph.D. dissertation that is very much self contained. This book consists of the following chapters:
Chapter 1: Preliminaries and Basic Concept
Covering fundamental definitions of mset, and its operations union, intersection, subtraction of two msets, power-set of a mset, and so on.
Chapter 2: Relations and Functions
Extension of classic relations and functions over classic set to mset.
Chapter 3: Partially Ordered Multisets - Chains and AntiChains
Chapter 4: Topologies on Multisets
Chapter 5: Generating Multiset Topologies using Multiset Relations
Chapter 6: Rough Multisets and Its Multiset
Chapter 7: Conclusion and Future Work
I am not a mathematician but an engineer so know the significant of Chapter 2. Most of chapters seems to be published by the authors in the high quality journals including "Information Science".
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