Filters and limits in filtered spaces

  • David Carf`ı Department of Mathematics, University of California Riverside

Abstract

In this lecture  notes,  we study filters and limits in a feasible  sufficiently general  way for  many  applications  to  Physics,  Economics and  Social  Science.    In particular  we analyze:



  • Filters;



  • Filter bases;



  • Basic example in topological  spaces;



  • Basic examples in preordered spaces;



  • Filtered spaces;



  • Induced filter bases;



  • Examples in topological spaces;



  • Examples on the real line;



  • Limits;



  • Limits with respect to filter bases;



  • Limits with respect to filter bases  on subspaces;



  • Limits and topology;



  • Limits of functions on topological  spaces;



  • Limits of functions on a topological  subspace;



  • Some basic theorems for topology;



  • Unicity of the limit in Hausdor spaces;



  • Limits and functionals;



  • Limits for real functional;



  • Limits and operations;



  • Local boundness;



  • Complements;



  • Limits and convergence of filtered bases;



  • Limit of composition.


 

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Carfì, D. and F. Musolino (2014b). Speculative and hedging interaction model in oil and U.S. dollar markets with _nancial transaction taxes. Economic Modelling 37 (0), 306-319. https://dx.doi.org/10.1016/j.econmod.2013.11.003

Carfì, D. and F. Musolino (2015a). A coopetitive-dynamical game model for currency markets stabilization. AAPP | Physical, Mathematical, and Natural Sciences 93 (1), 1{29. https://dx.doi.org/10.1478/AAPP.931C1

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Carfì, D. and E. Perrone (2013). Asymmetric Cournot Duopoly: A Game Complete Analysis. Journal of Reviews on Global Economics 2, 194-202. https://dx.doi.org/10.6000/1929-7092.2013.02.16

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Carfì, D. and A. Ricciardello (2010). An algorithm for payo_ space in C1- Games. AAPP | Physical, Mathematical, and Natural Sciences 88 (1), 1-19. https://dx.doi.org/10.1478/C1A1001003

Carfì, D. and A. Ricciardello (2011). Topics in Game Theory. Il Gabbiano. https://dx.doi.org/10.13140/RG.2.1.2368.9685

Carfì, D. and A. Ricciardello (2012a). Algorithms for Payoff Trajectories in C1 Parametric Games. In S. Greco, B. Bouchon-Meunier, G. Coletti, M. Fedrizzi, B. Matarazzo, and R. R. Yager (Eds.), Advances in Computational Intelligence (14th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2012, Catania, Italy, July 9-13, 2012, Proceedings, Part IV), Volume 300 of Communications in Computer and Information Science, pp. 642-654. Springer Berlin Heidelberg. https://dx.doi.org/10.1007/978-3-642-31724-8_67

Carfì, D. and A. Ricciardello (2012b). Topics in Game Theory. Applied Sciences - Monographs 9, Balkan Society of Geometers. http://www.mathem.pub.ro/apps/mono/A-09-Car.pdf

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Carfì, D. and A. Romeo (2015). Improving Welfare in Congo: Italian National Hydrocarbons Authority Strategies and its Possible Coopetitive Alliances with Green Energy Producers. Journal of Applied Economic Sciences 10 (4(34)), 571-592. http://cesmaa.eu/journals/jaes/files/JAES_summer%204(34)_online.pdf

Carfì, D. and D. Schilirò (2011). Crisis in the Euro Area. Coopetitive Game Solutions as New Policy Tools. Theoretical and Practical Research in Economic Fields 2 (1(3)), 23-36. http://www.asers.eu/journals/tpref/tpref-past-issues.html

Carfì, D. and D. Schilirò (2012a). A Framework of coopetitive games: Applications to the Greek crisis. AAPP | Physical, Mathematical, and Natural Sciences 90 (1), 1-32. https://dx.doi.org/10.1478/AAPP.901A1

Carfì, D. and D. Schilirò (2012b). A Model of Coopetitive Game for the Environmental Sustainability of a Global Green Economy. Journal of Environmental Management and Tourism 3 (1(5)), 5-17. http://journals.aserspublishing.eu/jemt/article/view/378

Carfì, D. and D. Schilirò (2012c). A coopetitive model for the green economy. Economic Modelling 29 (4), 1215-1219. https://dx.doi.org/10.1016/j.econmod.2012.04.005

Carfì, D. and D. Schilirò (2012d). Global Green Economy and Environmental Sustainability: A Coopetitive Model. In S. Greco, B. Bouchon-Meunier, G. Coletti, M. Fedrizzi, B. Matarazzo, and R. Yager (Eds.), Advances in Computational Intelligence (14th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2012, Catania, Italy, July 9-13, 2012, Proceedings, Part IV), Volume 300 of Communications in Computer and Information Science, pp. 593-606. Springer Berlin Heidelberg. https://dx.doi.org/10.1007/978-3-642-31724-8_63

Carfì, D. and D. Schilirò (2014). Improving Competitiveness and Trade Balance Of Greek Economy: A Coopetitive Strategy Model. Journal of Applied Economic Sciences 9 (2(28)), 211-220. http://www.ceeol.com/aspx/issuedetails.aspx?issueid=583d6083-2bbf-4d8c-af1f-3b5786c6e087&articleId=8c9be4cb-86d9-43f1-b555-58b8cb28bbeb

Donato, A. (2017). A multilinear interaction model: algorithms for Kalai-Smorodinsky solution. Journal of Mathematical Economics and Finance 3 (1(4)), 47-74. http://journals.aserspublishing.eu/jmef/article/view/1355

Okura, M. and D. Carfì (2014). Coopetition and Game Theory. Journal of Applied Economic Sciences 9 (3(29)), 458{469. http://cesmaa.eu/journals/jaes/files/JAES_2014_Fall.pdf#page=123
Published
2018-02-06
How to Cite
CARF`I, David. Filters and limits in filtered spaces. Journal of Mathematical Economics and Finance, [S.l.], v. 3, n. 2(5), p. 33 - 82, feb. 2018. ISSN 2458-0813. Available at: <https://journals.aserspublishing.eu/jmef/article/view/1736>. Date accessed: 05 july 2022. doi: https://doi.org/10.14505/jmef.v3.2(5).03.