This book contains selected chapters on recent research in topology. It bridges the gap between recent trends of topological theories and their applications in areas like social sciences, natural sciences, soft computing, economics, theoretical chemistry, cryptography, pattern recognitions and granular computing. There are 14 chapters, including two chapters on mathematical economics from the perspective of topology. The book discusses topics on function spaces, relator space, preorder, quasi-uniformities, bitopological dynamical systems, b-metric spaces and related fixed point theory. This book is useful to researchers, experts and scientists in studying the cutting-edge research in topology and related areas and helps them applying topology in solving real-life problems the society and science are facing these days.

Focuses on applications of topological theories in social sciences, natural sciences, and soft computing Discusses topics on bitopological dynamical systems, fuzzy topology, granular computing, and topological preferences Includes two chapters on mathematical economics from the perspective of topology

Autorentext
Santanu Acharjee is an Assistant Professor at the Department of Mathematics, Gauhati University, Guwahati, Assam, India. He did his M.Sc. and Ph.D. in Mathematics from Gauhati University. His research areas are topology, soft computing, arti cial intelligence, mathematical social science, mathematical economics, social networks, big data analytics, human traf cking and anti-terrorism research. He has published more than 30 research papers and 3 book chapters. Moreover, he has collaborated with several eminent researchers and visiting researchers of several international institutes: the Institute for Advanced Study, USA; the University of Oxford, UK; Creighton University, USA; the University of Auckland, New Zealand; Kuwait University; the University of California, Riverside, USA; the Russian Academy of Science; and the University of Debrecen, Hungary, etc. Dr. Acharjee was invited as a Visiting Researcher by the Fields Institute, Canada. He was awarded a travel grant by the National Board of Higher mathematics (NBHM). He jointly introduced a new area of mathematical research named "bitopological dynamical system" in the year 2020. He is a member of the American Mathematical Society (USA) and the International Association of Engineers (Hong Kong). He is also a life member of the Indian Science Congress Association (India). Dr. Acharjee is a reviewer for Mathematical Reviews (AMS), zbMATH Open (Germany), several journals of American Psychological Association as well as 38 other international journals of mathematics and interdisciplinary elds. He has edited special issues for some reputed journals as a guest editor. He jointly edited the book entitled *Advances in Mathematical Analysis *and its Applications. He has delivered more than 10 invited talks at various national and international conferences.

Inhalt
Chapter 1. Spaces of Minimal Usco and Minimal Cusco Maps as Fréchet Topological Vector Spaces.- Chapter 2. Contra Continuity Properties of Relations in Relator Spaces.- Chapter 3. The Continuous Representation Property in Utility Theory.- Chapter 4. On Quasi-Uniformities, Function Spaces and Atoms: remarks and some Questions.- Chapter 5. Some Cardinal Estimations via the Inclusion-Exclusion Principle in Finite T0 Topological Spaces.- Chapter 6. Representations of preference relations with preutility functions on metric spaces.- Chapter 7. Entropy of a pairwise continuous map in NWPC bitopological dynamical systems.- Chapter 8. Topological Approaches for Vector Variational Inequality Problems.- Chapter 9. Ideals and Grills associated with a Rough set.- Chapter 10. Filter verses ideal on topological spaces.- Chapter 11. Fisher Type Set-valued Mappings in b-metric spaces and an Application to Integral Inclusion.- Chapter 12. Topological aspects of granular computing.- Chapter 13. On topological index of naturally occurring zeolite material [4, n].- Chapter 14. q-Rung Orthopair Fuzzy Points and Applications to q-Rung Orthopair Fuzzy Topological Spaces and Pattern Recognition.