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Open Access Research Article

New types of connected, component spaces and maximal open set via s-operation

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pp. 481–495Vol. 27Issue 3April 2024DOI: 10.47974/JIM-1723XML
Received:
04 Jan 2023
Published Online:
07 May 2024
Article type:
Research Article
Language:
EN
Article no.:
JIM-1723
Pages:
481–495

Abstract

This paper aims to introduce a kind of connected space called λrc-connected. We analyze the characterizations, properties, and relationships of λrc-connected spaces with other types of connected spaces including, λrc-locally connected spaces. Additionally, we define a class of maximal open sets which called maximal λrc-open sets. Some of its basic properties, characterization and relationships are studied and obtained. 

Keywords

Subject Classifications

(2010) 54A0554B0554D05

References

[1] C. Carpintero, E. Rosas, M. Salas, J. Sanabria and L. Vasquez, “Generalization of ω-closed sets via operators and ideals”, Sarajevo Journal of Mathematics, Vol 9, No 2, pp. 293-301 (2013). https://www.anubih.ba/Journals/vol.9,no-2,y13/13Rosas-et-al.pdf.
[2] C. Carpintero, N. Rajesh and E. Rosas, “Operator approach on b–open sets and applications”, Bol. Soc. Paran. Mat. Vol. 30, No 1, pp. 21-33 (2012). http://www.spm.uem.br/bspm/pdf/vol30-1/Art2.pdf. 
[3] C. Carpintero, N. Rajesh and E. Rosas, “Operation via-regular open sets”, Italian Journal of Pure and Applied Mathematics, Vol 31, pp. 227-238 (2013). ISSN 2239-0227. https://ijpam.uniud.it/online_issue/201331/20-Carpintero-Rajesh-Rosas-2-final.pdf. 
[4] C. Dorsett, “Semi-connectedness”, Indian J. Mech. Math., 17(1), pp. 57- 63 (1979).
[5] S. Kasahara, “Operator-compact spaces”, Math., Japon., pp. 97-105 (1979).
[6] A. B. Khalaf and S. F. Namiq, “λ-Open Sets and λ-Separation Axioms in Topological Spaces”, Journal of Advanced Studies in Topology, Vol 4 (1), pp. 150-158 (2013). https://www.m-sciences.com/index.php/jast/issue/view/9. 
[7] N. Levine, “Semi-open sets and semi-continuity in topological spaces”, The American Mathematical Monthly, Vol 70(1), pp. 36-41 (1963). 
[8] S. F. Namiq, “New Types of Continuity and Separation Axiom Based Operation in Topological Spaces” (2011), Sulaimani.
[9] S. F. Namiq, “ λrc-Open Sets and Topological Properties”, (Submit) 
[10] S. F. Namiq, “ λ-Connected Spaces Via λ-Open Sets”, Journal of Garmian University, pp. 165-178 (2015).
[11] E. Rosas and S. F. Namiq, “On minimal λrc-open sets”, Italian Journal of Pure and Applied Mathematics, Vol 43, pp. 868-877 (2020). ISSN 2239-0227. https://ijpam.uniud.it/journal/onl_2020-43.htm 
[12] E. Rosas and S. F. Namiq, “On minimal λco-open sets”, Proyecciones Journal of Mathematics, Vol. 39(2), pp. 457-470 (2020). https://www.revistaproyecciones.cl/index.php/proyecciones/issue/view/308 
[13] E. Rosas and J. Vielma, “Operator-compact and operator-connected spaces”, Sci. Math., Vol. 1. no. 2, pp. 203-208 (1998). 
[14] R. Sen, “On generalized γµ-closed sets and related continuity”, Acta Univ. Sapientiae, Math., Vol. 13(2), pp. 483-493 (2021). https://www.emis.de/journals/AUSM/ 
[15] M. Stone, “Applications of the theory of Boolean rings to general topology”, Trans. Amer. Math. Soc., 41, pp.374-481 (1937).
[16] S. Willard, General topology. Addison-Wesley Publishing Company, Inc., Reading, Mass., (1970).

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