Characterizations of Almost \(\tau^\star(\sigma_1,\sigma_2)\)-Continuous Functions
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Abstract
This paper deals with the concept of almost \(\tau^\star(\sigma_1,\sigma_2)\)-continuous functions. Moreover, several characterizations and some properties concerning almost \(\tau^\star(\sigma_1,\sigma_2)\)-continuous functions are investigated. Furthermore, the relationships between \(\tau^\star(\sigma_1,\sigma_2)\)-continuity and almost \(\tau^\star(\sigma_1,\sigma_2)\)-continuity are considered.
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References
- M.E. Abd El-Monsef, E.F. Lashien, A.A. Nasef, On $mathscr{I}$-Open Sets and $mathscr{I}$-Continuity, Kyungpook Math. J. 32 (1992), 21–30.
- M.E. Abd El-Monsef, S.N. El-Deeb, R.A. Mahmoud, $beta$-Open Sets and $beta$-Continuous Mappings, Bull. Fac. Sci. Assiut Univ. 12 (1983), 77–90.
- W. Al-Omeri, T. Noiri, On Almost $e$-$mathscr{I}$-Continuous Functions, Demonstr. Math. 54 (2021), 168–177. https://doi.org/10.1515/dema-2021-0014.
- D. Andrijevi'{c}, On $b$-Open Sets, Mat. Vesnik 48 (1996), 59–64.
- C. Boonpok, $pimath$-Continuity and Weak $pimath$-Continuity, Carpathian Math. Publ. 17 (2025), 171–186. https://doi.org/10.15330/cmp.17.1.171-186.
- C. Boonpok, P. Pue-On, Characterizations of Almost $(tau_1,tau_2)$-Continuous Functions, Int. J. Anal. Appl. 22 (2024), 33. https://doi.org/10.28924/2291-8639-22-2024-33.
- C. Boonpok, C. Klanarong, On Weakly $(tau_1,tau_2)$-Continuous Functions, Eur. J. Pure Appl. Math. 17 (2024), 416–425. https://doi.org/10.29020/nybg.ejpam.v17i1.4976.
- C. Boonpok, P. Pue-on, Upper and Lower Weakly $alpha$-$star$-Continuous Multifunctions, Int. J. Anal. Appl. 21 (2023), 90. https://doi.org/10.28924/2291-8639-21-2023-90.
- C. Boonpok, N. Srisarakham, $(tau_1,tau_2)$-Continuity for Functions, Asia Pac. J. Math. 11 (2024), 21. https://doi.org/10.28924/APJM/11-21.
- C. Boonpok, on Some Spaces via Topological Ideals, Open Math. 21 (2023), 20230118. https://doi.org/10.1515/math-2023-0118.
- C. Boonpok, $theta(star)$-Precontinuity, Mathematica, 65 (2023), 31–42. https://doi.org/10.24193/mathcluj.2023.1.04.
- C. Boonpok, Weak Openness and Weak Continuity in Ideal Topological Spaces, Mathematica, 64 (2022), 173–185.
- C. Boonpok, $(tau_1,tau_2)delta$-Semicontinuous Multifunctions, Heliyon, 6 (2020), e05367. https://doi.org/10.1016/j.heliyon.2020.e05367.
- C. Boonpok, C. Viriyapong, M. Thongmoon, on Upper and Lower $(tau_1,tau_2)$-Precontinuous Multifunctions, J. Math. Computer Sci. 18 (2018), 282–293. https://doi.org/10.22436/jmcs.018.03.04.
- M. Chiangpradit, S. Sompong, C. Boonpok, Weakly Quasi $(tau_1,tau_2)$-Continuous Functions, Int. J. Anal. Appl. 22 (2024), 125. https://doi.org/10.28924/2291-8639-22-2024-125.
- E. Hatir and T. Noiri, On $beta$-$mathscr{I}$-Open Sets and a Decomposition of Almost $mathscr{I}$-Continuity, Bull. Malays. Math. Sci. Soc. 29 (2006), 119–124.
- D. Jankovic, T.R. Hamlet, New Topologies from Old via Ideals, Am. Math. Mon. 97 (1990), 295–310. https://doi.org/10.2307/2324512.
- A. Keskin, T. Noiri, Almost $b$-Continuous Functions, Chaos Solitons Fractals, 41 (2009), 72–81. https://doi.org/10.1016/j.chaos.2007.11.012.
- J. Khampakdee, A. Sama-Ae, C. Boonpok, Upper and Lower Continuous Multifunctions Defined Between an Ideal Topological Space and a Bitopological Space, Eur. J. Pure Appl. Math. 18 (2025), 6565. https://doi.org/10.29020/nybg.ejpam.v18i3.6565.
- B. Kong-ied, A. Sama-Ae, C. Boonpok, Almost Quasi $tau^star(sigma_1,sigma_2)$-Continuous and Weakly Quasi $tau^star(sigma_1,sigma_2)$-Continuous Functions, Eur. J. Pure Appl. Math. 18 (2025), 6572. https://doi.org/10.29020/nybg.ejpam.v18i3.6572.
- B. Kong-ied, S. Sompong, C. Boonpok, Almost Quasi $(tau_1,tau_2)$-Continuous Functions, Asia Pac. J. Math. 11 (2024), 64. https://doi.org/10.28924/APJM/11-64.
- K. Kuratowski, Topology, Academic Press, 1966.
- S.N. Maheshwari, G.I. Chae, P.C. Jain, Almost Feebly Continuous Functions, Ulsan Inst. Tech. Rep. 13 (1982), 195–197.
- S. Marcus, Sur les Fonctions Quasicontinues au Sens de S. Kempisty, Colloq. Math. 8 (1961), 47–53. https://eudml.org/doc/210887.
- A.S. Mashhour, M.E. Abd El-Monsef, S. N. El-Deeb, On Precontinuous and Weak Precontinuous Mappings, Proc. Math. Phys. Soc. Egypt 53 (1982), 47–53.
- B.M. Munshi, D.S. Bassan, Almost Semi-Continuous Mappings, Math. Student, 49 (1981), 239–248.
- A.A. Nasef, T. Noiri, Some Weak Forms of Almost Continuity, Acta Math. Hungar. 74 (1997), 211–219.
- T. Noiri, V. Popa, On $(mI,nJ)$-Continuous Multifunctions, Rom. J. Math. Comput. Sci. 15 (2025), 1–8.
- T. Noiri, Almost $alpha$-Continuous Functions, Kyungpook Math. J. 28 (1988), 71–77.
- V. Popa, On a Decomposition of Quasicontinuity in Topological Spaces, Stud. Cerc. Mat. 30 (1978), 31–35.
- M.K. Singal, A.R. Singal, Almost Continuous Mappings, Yokohama J. Math. 16 (1968), 63–73.
- M. Thongmoon, S. Sompong, C. Boonpok, $(tau_1,tau_2)$-Continuous Multifunctions and $tau_1tau_2$-$delta$-Open Sets, Int. J. Math. Comput. Sci. 19 (2024), 1369–1375.
- N. Viriyapong, A. Sama-Ae, C. Boonpok, On Almost $tau^star(sigma_1,sigma_2)$-Continuity and Weak $tau^star(sigma_1,sigma_2)$-Continuity, Eur. J. Pure Appl. Math. 18 (2025), 6568. https://doi.org/10.29020/nybg.ejpam.v18i3.6568.
- N. Viriyapong, S. Sompong, C. Boonpok, Upper and Lower $s$-$(tau_1,tau_2)p$-Continuous Multifunctions, Eur. J. Pure Appl. Math. 17 (2024), 2210–2220. https://doi.org/10.29020/nybg.ejpam.v17i3.5322.
- N. Viriyapong, S. Sompong, C. Boonpok, $(tau_1,tau_2)$-Extremal Disconnectedness in Bitopological Spaces, Int. J. Math. Comput. Sci. 19 (2024), 855–860.
- C. Viriyapong, C. Boonpok, $(tau_1,tau_2)alpha$-Continuity for Multifunctions, J. Math. 2020 (2020), 6285763. https://doi.org/10.1155/2020/6285763.
- S. Y"{u}ksel, A. Ac{c}ikg"{o}z, T. Noiri, On $delta$-$mathscr{I}$-Continuous Functions, Turk. J. Math. 29 (2005), 39–51.