Other forms of continuity modulo an ideal

Pachón Rubiano, Néstor Raúl; Pachón Rubiano, Néstor Raúl

doi:10.22199/issn.0717-6279-2020-05-0075

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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.39 no.5 Antofagasta 2020

http://dx.doi.org/10.22199/issn.0717-6279-2020-05-0075

Artículos

Other forms of continuity modulo an ideal

Néstor Raúl Pachón Rubiano¹
http://orcid.org/0000-0002-7191-127X

^¹Escuela Colombiana de Ingeniería Julio Garavito, Dept of Mathematics, Bogotá, Colombia. E.mail: nestor.pachon@escuelaing.edu.co

Abstract

The topic analized in this paper is the continuity modulo an ideal. We use the open-I sets to introduce new forms of weak continuity. Some basic properties of C-continuous and D-continuous functions will be investigated, as well as some applications related to compactness and separability. All the results obtained in this work constitute generalizations of well-known results of the general topology. We prove that these new concepts are independent of other forms of weak continuity, modulo an ideal, introduced by Abd El-Monsef, Özkurt, Çobankaya and Kaniewski.

Keywords: ℐ-continuous; ℐ -compact; ℐ -normal

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Acknowledgment

Research supported by the Escuela Colombiana de Ingeniería Julio Garavito.

References

[1] M. E. Abd El-Monsef, E. F. Lashien, and A. A. Nasef, “On I-open sets and I-continuous functions”, Kyungpook mathematical journal, vol. 32, no. 1, pp. 21-30, Jun. 1992. [On line]. Available: https://bit.ly/3mP7S7l [ Links ]

[2] A. Çobankaya, F. Kuyucu, and S. Kilinç, “New approaches about I-continuous functions in ideal topological spaces”, International journal of pure and applied mathematics, vol. 113, no. 2 , pp. 291-297, 2017. [On line]. Available: https://bit.ly/2FNfmqs [ Links ]

[3] M. K. Gupta and T. Noiri, “C-compactness modulo an ideal”, International journal of mathematics and mathematical sciences, Art ID. 078135, 2006, doi: 10.1155/IJMMS/2006/78135 [ Links ]

[4] D. Jancovic and T. R. Hamlett, “Compatible extensions of ideals”, Unione Matematica Italiana Bollettino. B. Serie 7, vol. 6, no. 3, pp. 453-465, 1992. [ Links ]

[5] D. Jancovic and T. R. Hamlett, “New topologies from old via ideals”, The american mathematical monthly, vol. 97, no. 4, pp. 295-310, Apr. 1990, doi: 10.1080/00029890.1990.11995593 [ Links ]

[6] J. Kaniewski and Z. Piotrowski, “Concerning continuity apart from a meager set”, Proceedings of the American Mathematical Society, vol. 98, no. 2, pp. 324-328, 1986, doi: 10.1090/S0002-9939-1986-0854041-3 [ Links ]

[7] R. Newcomb, "Topologies which are compact modulo an ideal", Ph.D. dissertation, University of California at Santa Barbara, 1967. [ Links ]

[8] A. Özkurt, “Some generalizations of local continuity in ideal topological spaces”, Scientific Studies and Research. Series Mathematics and Informatics (Online), vol. 24, no. 1, pp. 75-80, 2014. [On line]. Available: https://bit.ly/3hSC7pS [ Links ]

[9] N. R. Pachón Rubiano, “New forms of strong compactness in terms of ideals”, International journal of pure and applied mathematics , vol. 106, no. 2, pp. 481-493, 2016, doi: 10.12732/ijpam.v106i2.12 [ Links ]

[10] N. R. Pachón Rubiano,”Between closed and Ig-closed sets”, European journal of pure and applied mathematics, vol. 11, no. 1, p. 299, Jan. 2018, doi: 10.29020/nybg.ejpam.v11i2.3131 [ Links ]

[11] J. Porter and J. Thomas, “On _H-closed and minimal Hausdorff spaces”, Transactions of the American Mathematical Society, vol. 138, pp. 159-170, 1969, doi: 10.1090/S0002-9947-1969-0238268-4 [ Links ]

[12] V. Renukadevi and D. Sivaraj, “A generalization of normal spaces”, Archivum mathematicum, vol. 44, no. 4, pp. 265-270, 2008. [On line]. Available: https://bit.ly/2FSj9To [ Links ]

[13] S. Suriyakala and R. Vembu, “On separation axioms in ideal topological spaces”, Malaya journal of matematik, vol. 4, no. 2, pp. 318-324, 2016. [On line]. Available: https://bit.ly/3iWOdji [ Links ]

Received: August 31, 2019; Accepted: January 31, 2020

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