Bioperation approach to Przemski’s decomposition theorems

Carpintero, C.; Nirmala, R.; Rajesh, N.; Rosas, E.; Carpintero, C.; Nirmala, R.; Rajesh, N.; Rosas, E.

doi:10.22199/issn.0717-6279-2020-05-0073

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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.0717-6279-2020-05-0073

Artículos

Bioperation approach to Przemski’s decomposition theorems

C. Carpintero¹
http://orcid.org/0000-0003-3831-952X

R. Nirmala²
http://orcid.org/0000-0003-0114-6370

N. Rajesh³

E. Rosas⁴
http://orcid.org/0000-0001-8123-9344

^¹Corporación Universitaria del Caribe-CECAR, Sincelejo, Colombia. e-mail: carpintero.carlos@gmail.com

^²Rajah Serfoji Government College (Autonomous). Dept. of Mathematics, Namakkal, TN, India. e-mail: nirmala.karthik143@gmail.com

^³Rajah Serfoji Government College (Autonomous). Department of Mathematics, Namakkal, TN, India. e-mail: nrajesh@gmail.com

^⁴Universidad de la Costa, Dept. de Ciencias Naturales y Exactas, Barranquilla, Colombia. e-mail: ennisrafael@gmail.com

Abstract

Przemski introduced D(α, s)-set, D(α, b)-set, D(p, sp)-set, D(p, b)- set and D(b, sp)-set to obtain several decompositions of continuity. In this paper, we extend these sets via bioperation and obtain new decompositions of continuity.

Keywords: Topological spaces; γ ∨ γ’-open set

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References

[1] S. Kasahara, “Operation-compact spaces”, Mathematics japonica, vol. 24, pp. 97-105, 1979. [ Links ]

[2] R. Nirmala and N. Rajesh, “Bioperation-regular open sets”, Aryabhata journal mathematics informatics, vol. 8, no. 1, pp. 53-62, 2016. [ Links ]

[3] R. Nirmala and N. Rajesh, “Generalization of semiopen sets via bioperation”(under preparation). [ Links ]

[4] H. Ogata and H. Maki, “Bioperation on topological spaces”, Mathematics japonica , vol. 38, no. 5, pp. 981-985, 1993. [ Links ]

[5] M. Perzemshi, “A decomposition of continuity and α-continuity”, Acta mathematica hungarica, vol. 61, no. 1/2, pp. 93-98, 1993, doi: 10.1007/BF01872101 [ Links ]

Received: July 31, 2019; Accepted: November 30, 2019

This is an open-access article distributed under the terms of the Creative Commons Attribution License