Topological aspects of continuity via generalized limit
DOI:
https://doi.org/10.14393/BEJOM-v2-n3-2021-55291Keywords:
limit, continuity, topological invariant.Abstract
This article aims to introduce the concept of generalized continuity of an function with respect to another function and to analyze the topological aspects of this concept Initially, the article presents the concept and the properties of generalized limit ofan function with respect to another function, highlighting that the Riemann integral is a particular case of generalized limit. Then, the definition of generalized continuity is presented, evidencing that this concept does not coincide with the classical continuity, being the last one a particular case of the first. Finally, some topological aspects associated with the concept of generalized continuity are approached in order to present proofs about the preservation of topological invariants via generalized continuity, such as preservation of compactness and connectedness.Downloads
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BOTELHO, G. M. A.; PELLEGRINO, D. M.; TEIXEIRA, E. V. Fundamentos de Análise Funcional, 2. ed. Rio de Janeiro: Ed. SBM, 2015.
BRAZ, J. H. S.; VIEIRA, M. G. O. Limites generalizados de funções, In: V SEMAP, n. 5, 2014. Anais da V SEMAP. Available in:http://www.semap.facip.ufu.br/node/30. Accessed on 11/19/2020.
COLONIUS, F.; KIZIL E.; SAN MARTIN L. A. B. Covering space for monotonichomotopy of trajectories of control system. J. Differential Equations, v. 216, n. 2, p. 324-353, 2005.
KÜHLKAMP, N. Introdução à Topologia Geral, 2. ed. Florianópolis: Ed. daUFSC, 2002.
KUPKA, I. On similarity of functions, Top. Proc., v. 36, p. 173-187, 2010.
KUPKA, I. Similar functions and their properties, Tatra Mt. Math. Publ., v. 55, p.47-56, 2013.
KUPKA, I. Measurability of similar functions, Ann. Acad. Sci. Fenn. Math. Diss.,v. 42, p. 803-808, 2017.
KUPKA, I. Generalized derivative and generalized continuity, Tatra Mt. Math. Publ., v. 74, p. 77-84, 2019.
MUNKRES, J. R.Topology, 2. ed. London: Pearson, 2013.
VIEIRA, M. G. O.; KIZIL, E; CATUOGNO, P. J. Monotonic homotopy for trajectories of Young systems. J. Dyn. Control Syst., v. 19, n. 3, p. 405-420, 2013.
VIEIRA, M. G. O.; KIZIL, E; CATUOGNO, P. J. Regular trajectories of Youngsystems. J. Dyn. Control Syst., v. 21, n. 1, p. 1-21, 2015.
VIEIRA, M. G. O. Continuidade no contexto de limites generalizados, In: VII SEMAP, n. 7, 2016. Anais da VII SEMAP. Available in: http://www.semap.facip.ufu.br/node/69. Accessed on 11/19/2020.
WILLARD, S.General Topology, Reading, Massachusetts: Addison-Wesley Publishing Company, 1970.
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