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RETRACTED CHAPTER: “On faintly sp-\(\theta\) (semi-pre-\(\theta)\)-continuous functions”. (English) Zbl 1512.54016

Balasubramaniam, P. (ed.) et al., Mathematical modelling and scientific computation. Proceedings of the 2nd international conference, ICMMSC 2012, Gandhigram, Tamil Nadu, India, March 16–18, 2012. Berlin: Springer. Commun. Comput. Inf. Sci. 283, 22-31 (2012).
Summary: In this paper we introduce and study two new notions of faintly continuity which are called faintly sp-\(\theta\)-Continuous functions and faintly semi-pre-\(\theta\)-Continuous functions using the concept of b-\(\theta\) open sets and \(\beta-\theta\) open sets, the class of faintly sp-\(\theta\)-Continuous functions is a generalization of faintly Pre-\(\theta\) (Semi-\(\theta)\)-Continuous functions due to A. a. El-Atik [Thai J. Math. 9, No. 1, 83–93 (2011; Zbl 1261.54004)]. At the same time, the class of faintly semi-pre-\(\theta\)-Continuous functions is a generalization of faintly Pre-\(\theta\) (Semi-\(\theta)\)-Continuous functions and faintly sp-\(\theta\)-Continuous functions. Some characterizations and several properties concerning faintly sp-\(\theta\)-Continuous functions and faintly semi-pre-\(\theta\)-Continuous functions are obtained. Furthermore the relationships among these notions and other well-known forms of faintly continuity are also given.
Editorial remark. According to the retraction note (see [Zbl 07584160]) this paper “ha[s] been retracted for reasons of plagiarism. In addition, the name of the second author was added without his knowledge or consent.”
For the entire collection see [Zbl 1242.00059].

MSC:

54C08 Weak and generalized continuity
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References:

[1] El-Atik, A.A.: On Some Types of Faint Continuity. Thai Journal of Mathematics 9(1), 83-93 (2011) · Zbl 1261.54004
[2] Long, P.E., Herrington, L.L.: The \(T_{}θ\) -topology and Faintly Continuous Functions. Kyungpook Math. J. 22, 7-14 (1982) · Zbl 0486.54009
[3] Noiri, T., Popa, V.: Weak Forms of Faint Continuity. Bull. Math. Soc. Math. Roumanie. 34(82), 270-363 (1990) · Zbl 0739.54003
[4] Noiri, T.: Weak and Strong Forms of \(β\)-Irresolute Functions. Acta. Math. Hungar. 99, 315-328 (2003) · Zbl 1051.54011 · doi:10.1023/A:1024687630089
[5] Park, J.H.: Strongly \(θ-b\)-Continuous Functions. Acta. Math. Hungar. 110(4), 347-359 (2006) · Zbl 1104.54006 · doi:10.1007/s10474-006-0021-0
[6] Njástad: On Some Classes of Nearly Open Sets. Pacfic. J. Math. 15, 961-970 (1965) · Zbl 0137.41903 · doi:10.2140/pjm.1965.15.961
[7] Noiri, T., Popa, V.: Almost Weakly Continuous Multifunctions. Demonstratio. Math. 26, 363-380 (1993) · Zbl 0859.54007
[8] Mashhour, A.S., Abd El-Monsef, M.E., El-Deeb, S.N.: On Precontinuous and Weak Precontinuous Mappings. Proc. Math. Phy. Soc. 53, 47-53 (1982) · Zbl 0571.54011
[9] Abd El-Monsef, M.E., El-Deeb, S.N., Mahmoud, R.A.: \(β\)-Open Sets and \(β\)-Continuous Mappings. Bull. Fac. Sci. Assiut. Univ. 12(1), 77-90 (1983) · Zbl 0577.54008
[10] Andrijevic, D.: Semi-Pre Open Sets. Mat. Vesnik. 38, 24-32 (1986) · Zbl 0604.54002
[11] El-Atik, A.A.: A Study of Some Types of Mappings on Topological Spaces. M. Sc. Thesis, Tanta Uni. Egypt (1997)
[12] Andrijević, D.: On b-Open Sets. Mat. Bech. 48, 59-64 (1996) · Zbl 0885.54002
[13] Dontchev, J., Przemski, M.: On the Various Decompositions of Continuous and Some Weakly Continuous Functions. Acta. Math. Hungar. 71(1-2), 109-120 (1996) · Zbl 0852.54012 · doi:10.1007/BF00052199
[14] Crossley, S.G., Hildebrand, S.K.: Semi-Closure. Texas. J. Sci. 22, 99-112 (1971)
[15] El-Deeb, S.N., Hasanein, I.A., Mashhour, A.S., Noiri, T.: On p-Regulars Spaces. Bull. Math. Soc. Math. R. S. Roumanie. 27(75), 311-315 (1983) · Zbl 0524.54016
[16] Levine, N.: Semi-Open Sets and Semi-Continuity in Topological Spaces. Amer. Math. Monthly 70, 36-41 (1963) · Zbl 0113.16304 · doi:10.2307/2312781
[17] Jafari, S., Noiri, T.: On Faintly \(α\)-Continuous Functions. Indian. J. Math. 42, 203-210 (2000) · Zbl 1033.54503
[18] Nasef, A.A.: Another Weak Forms of Faint Continuity. Chaos, Solitons & Fractals 12, 2219-2225 (2001) · Zbl 0996.54016 · doi:10.1016/S0960-0779(00)00156-9
[19] Noiri, T., Popa, V.: Faintly m-Continuous Functions. Chaos, Solitons & Fractals 19, 1147-1159 (2004) · Zbl 1079.54507 · doi:10.1016/S0960-0779(03)00303-5
[20] Noiri, T.: On \(δ\)-Continuous Functions. J. Korean. Math. Soc. 16, 161-166 (1980) · Zbl 0435.54010
[21] Zorlutuna, İ.: On b-Closed Space and \(θ\)-b-Continuous Functions. The Arabian Journal for Science and Engineering 34(2A), 205-216 (2009)
[22] Noiri, T., Popa, V.: Strongly \(θ-β\)-Continuous Functions. J. Pure Math. 19, 31-39 (2002) · Zbl 1267.54014
[23] Levine, N.: A Decomposition of Continuity in Topological Spaces. Amer. Math. Monthly 63, 44-66 (1961) · Zbl 0100.18601 · doi:10.2307/2311363
[24] Janković, D.: \(θ\)-Regular Spaces. Int. J. Math. Sci. 8, 615-624 (1985) · Zbl 0577.54012 · doi:10.1155/S0161171285000667
[25] Rajesh, N., Salleh, Z.: Some More Results on b-\(θ\)-Open Sets. Buletinul Academiei De Stiinte A Rebublicii Moldova. Matematica. 3(61), 70-80 (2009) · Zbl 1186.54003
[26] Rose, D.A.: Weak Continuity and Strongly Closed Sets. Int. J. Math. Sci. 7(4), 809-825 (1984) · Zbl 0592.54013 · doi:10.1155/S0161171284000831
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