Sets and functions in terms of local function
Sets and functions in terms of local function
Keywords:
b-open sets, Local function, b*-continuous function, Homeomorphism
Abstract
In this paper, a collection of sets are investigated in such a way that the collection splits in the collection of preopen sets and the collection of b-open sets and also splits in the collection of semi-open sets and the collection of b-open sets. Functions in terms of this sets is a part of this paper and it will be considered that these collection remains invariant under homeomorphic image.
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References
A. Al-Omari and T. Noiri, Local closure functions in ideal topological spaces, Novi Sad J. Math., 43(2) (2013), 139-149.
A. Al-Omari and M. Noorani, Decomposition of continuity via b-open set, Bol. Soc. Paran. Mat., 26(1-2) (2008), 53-64.
A. Al-Omari and M. Noorani, On generalized b-closed sets, Bull. Malays. Math. Sci. Soc., 32(1) (2009), 19-30.
Z. A. Ameen, On types of generalized closed sets, J. Taibah Univ. Sci., 12(3) (2018), 290-293.
D. Andrijevic´, Semi-preopen sets, Mat. Vesnik, 38(1986), 24-32.
D. Andrijevic´, On b-open sets, Mat. Vesnik, 48: 59-64.
C. Bandyopadhyay and S. Modak, A new topology via Ψ-operator, Proc. Nat. Acad. Sci. India, 76(A)(IV)(2006), 317-320.
M. Caldas, S. Jafari and R. M. Latif, Applications of b-open sets and (b, s)-continuous funcions, King Fahd University of Petroleum and Min-erals. Dept. of Math. Sci. Technical Report Series, TR 400(2008).
C. Carpintero, N. Rajesh and E. Rosas, Operation-b-open sets in topological spaces, Fasc. Math., 48(2012), 13-21.
E. Ekici and M. Caldas, Slightly γ-continuous functions, Bol. Soc. Paran. Math., 22(2)(2004), 63-74.
M. E. El-Monsef, A. A. A. El-Atik and M. M. El-Sharkasy, Some topologies induced by b- open sets, Kyungpook Math. J., 45(2005), 539-547.
M. Ganster and M. Steiner, On some questions about b-open sets, Questions Answers Gen. Topology, 25(1)(2007), 45-52.
T. R. Hamlett and D. Jankovic´, Ideals in Topological Spaces and the Set Operator Ψ, Boll. U.M.I., 7(4-B)(1990), 863-874.
H. Hashimoto, On the *-topology and its applications, Fund. Math., 91(1976), 5-10.
E. Hatir and T. Noiri, On decomposition of continuity via idealization, Acta Math. Hungar, 96(2002), 341-349.
E. Hayashi, Topologies defined by local properties, Math. Ann., 156(1964), 205-215.
H. Z. Ibrahim, Bc-open sets in topological spaces, Advances in Pure Math., 3(2013), 34-40.
D. Jankovic´ and T. R. Hamlett, New topologies from old via ideals, Amer. Math. Monthly, 97(1990), 295-310.
D. Jankovic´ and T. R. Hamlett, Compatible extensions of ideals, Boll. U.M.I., 7(6-B)(1992), 453-465.
A. Keskin, T. Noiri and S. Yuksel, -sets and decomposition of C-continuity, Acta Math. Hungar., 104(2004), 307-313.
A. Keskin, T. Noiri and S. Yuksel, Idealization of decomposition theorem, Acta Math. Hungar., 102(2004), 269-277.
A. Keskin, T. Noiri and S. Yuksel, A note on -sets and -continuous functions, Acta Math. Hungar., 107(4)(2005), 287-293.
K. Kuratowski, Topology, Vol. I., Academic Press, New York (1966).
N. Levine, Semi-Open Sets and Semi-Continuity in Topological Spaces, Amer. Math. Monthly, 70(1)(1963), 36-41.
A. S. Mashhour, M. E. A. El-Monsef and S. N. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. [Egypt], 53(1982), 47-53.
S. Modak, Some new topologies on ideal topological spaces, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci, 82(3)(2012), 233-243.
S. Modak and C. Bandyopadhyay, A note on Ψ- operator, Bull. Malyas. Math. Sci. Soc., 30(1)(2007), 43-48.
S. Modak and Md. M. Islam, On * and Ψ operators in topological spaces with ideals, Trans. A. Razmadze Math. Inst., 172(2018), 372-377.
A. A. Nasef, On b-locally closed sets and related topics, Chaos, Solitons and Fractals., 12(2001), 1909-1915.
T. Natkaniec, On -continuity and -semicontinuity points, Math. Slovaca., 36(3)(1986), 297-312.
O. Njastad, On some classes of nearly open sets, Pacific J. Math., 15(3)(1965), 961-970.
Sk. Selim, T. Noiri and S. Modak, Ideals and associated filters on topological spaces, Eurasian Bull. Math., 2(3)(2019), 80-85.
R. Vaidyanathswamy, The localisation theory in set topology, Proc. India Acad. Sci., 20(1945), 51-61.
I. Zorlutuna, On b-closed spaces and -b-continuous functions, The Arab. J. Sci. Eng., 34(2A)(2009), 205-216.
A. Al-Omari and M. Noorani, Decomposition of continuity via b-open set, Bol. Soc. Paran. Mat., 26(1-2) (2008), 53-64.
A. Al-Omari and M. Noorani, On generalized b-closed sets, Bull. Malays. Math. Sci. Soc., 32(1) (2009), 19-30.
Z. A. Ameen, On types of generalized closed sets, J. Taibah Univ. Sci., 12(3) (2018), 290-293.
D. Andrijevic´, Semi-preopen sets, Mat. Vesnik, 38(1986), 24-32.
D. Andrijevic´, On b-open sets, Mat. Vesnik, 48: 59-64.
C. Bandyopadhyay and S. Modak, A new topology via Ψ-operator, Proc. Nat. Acad. Sci. India, 76(A)(IV)(2006), 317-320.
M. Caldas, S. Jafari and R. M. Latif, Applications of b-open sets and (b, s)-continuous funcions, King Fahd University of Petroleum and Min-erals. Dept. of Math. Sci. Technical Report Series, TR 400(2008).
C. Carpintero, N. Rajesh and E. Rosas, Operation-b-open sets in topological spaces, Fasc. Math., 48(2012), 13-21.
E. Ekici and M. Caldas, Slightly γ-continuous functions, Bol. Soc. Paran. Math., 22(2)(2004), 63-74.
M. E. El-Monsef, A. A. A. El-Atik and M. M. El-Sharkasy, Some topologies induced by b- open sets, Kyungpook Math. J., 45(2005), 539-547.
M. Ganster and M. Steiner, On some questions about b-open sets, Questions Answers Gen. Topology, 25(1)(2007), 45-52.
T. R. Hamlett and D. Jankovic´, Ideals in Topological Spaces and the Set Operator Ψ, Boll. U.M.I., 7(4-B)(1990), 863-874.
H. Hashimoto, On the *-topology and its applications, Fund. Math., 91(1976), 5-10.
E. Hatir and T. Noiri, On decomposition of continuity via idealization, Acta Math. Hungar, 96(2002), 341-349.
E. Hayashi, Topologies defined by local properties, Math. Ann., 156(1964), 205-215.
H. Z. Ibrahim, Bc-open sets in topological spaces, Advances in Pure Math., 3(2013), 34-40.
D. Jankovic´ and T. R. Hamlett, New topologies from old via ideals, Amer. Math. Monthly, 97(1990), 295-310.
D. Jankovic´ and T. R. Hamlett, Compatible extensions of ideals, Boll. U.M.I., 7(6-B)(1992), 453-465.
A. Keskin, T. Noiri and S. Yuksel, -sets and decomposition of C-continuity, Acta Math. Hungar., 104(2004), 307-313.
A. Keskin, T. Noiri and S. Yuksel, Idealization of decomposition theorem, Acta Math. Hungar., 102(2004), 269-277.
A. Keskin, T. Noiri and S. Yuksel, A note on -sets and -continuous functions, Acta Math. Hungar., 107(4)(2005), 287-293.
K. Kuratowski, Topology, Vol. I., Academic Press, New York (1966).
N. Levine, Semi-Open Sets and Semi-Continuity in Topological Spaces, Amer. Math. Monthly, 70(1)(1963), 36-41.
A. S. Mashhour, M. E. A. El-Monsef and S. N. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. [Egypt], 53(1982), 47-53.
S. Modak, Some new topologies on ideal topological spaces, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci, 82(3)(2012), 233-243.
S. Modak and C. Bandyopadhyay, A note on Ψ- operator, Bull. Malyas. Math. Sci. Soc., 30(1)(2007), 43-48.
S. Modak and Md. M. Islam, On * and Ψ operators in topological spaces with ideals, Trans. A. Razmadze Math. Inst., 172(2018), 372-377.
A. A. Nasef, On b-locally closed sets and related topics, Chaos, Solitons and Fractals., 12(2001), 1909-1915.
T. Natkaniec, On -continuity and -semicontinuity points, Math. Slovaca., 36(3)(1986), 297-312.
O. Njastad, On some classes of nearly open sets, Pacific J. Math., 15(3)(1965), 961-970.
Sk. Selim, T. Noiri and S. Modak, Ideals and associated filters on topological spaces, Eurasian Bull. Math., 2(3)(2019), 80-85.
R. Vaidyanathswamy, The localisation theory in set topology, Proc. India Acad. Sci., 20(1945), 51-61.
I. Zorlutuna, On b-closed spaces and -b-continuous functions, The Arab. J. Sci. Eng., 34(2A)(2009), 205-216.
Published
2022-03-24
How to Cite
Modak, S., Selim, S., & Islam, M. M. (2022). Sets and functions in terms of local function. Al-Qadisiyah Journal of Pure Science, 27(1), Math 91-102. https://doi.org/10.29350/qjps.2022.27.1.1483
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Section
Mathematics
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