Banerjee, Amar Kumar; Pal, Jagannath New separation axioms in generalized bitopological spaces. (English) Zbl 1452.54002 Math. Sci., Springer 14, No. 2, 185-192 (2020). Summary: Here, we have studied the ideas of \((s, t)\)-\(g_{\rho }\) and \((s, t)\)-\(\lambda_{\rho }\)-closed sets (\(s,t=1,2\); \(s\not =t\)) and pairwise \(\lambda \)-closed sets in a generalized bitopological space \((X,{\rho_1}, {\rho_2})\). We have investigated the properties on some new separation axioms namely pairwise \(T_\frac{1}{4} \), pairwise \(T_\frac{3}{8} \), pairwise \(T_\frac{5}{8}\) and have established mutual relations with pairwise \(T_0\), pairwise \(T_\frac{1}{2}\) and pairwise \(T_1\). Also we have shown that under certain conditions, these axioms are equivalent. Cited in 1 Document MSC: 54A05 Topological spaces and generalizations (closure spaces, etc.) 54D10 Lower separation axioms (\(T_0\)–\(T_3\), etc.) Keywords:\((s; t)\)-\(\lambda_{\rho }\)-closed set; pairwise \(\lambda \)-closed set; pairwise \(T_\frac{1}{4} \); pairwise \(T_\frac{3}{8} \); pairwise \(T_\frac{5}{8} \); pairwise \(T_\frac{1}{2} \); pairwise \(\lambda \)-symmetric spaces PDFBibTeX XMLCite \textit{A. K. Banerjee} and \textit{J. Pal}, Math. Sci., Springer 14, No. 2, 185--192 (2020; Zbl 1452.54002) Full Text: DOI arXiv References: [1] Alexandroff, AD, Additive set functions in abstract space, Math. Sb. (N.S.), 8, 50, 307-348 (1940) · JFM 66.0218.01 [2] Banerjee, AK; Saha, PK, Preopen sets in bispace, South East Asian J. Math.Math. Sci., 13, 2, 63-74 (2017) [3] Banerjee, AK; Saha, PK, Semi open sets in bispaces, CUBO Math. J., 17, 1, 99-106 (2015) · Zbl 1326.54006 [4] Banerjee, AK; Saha, PK, Bispace group, Int. J. Math. Sci. Eng. Appl. (IJMSEA), 5, V, 41-47 (2011) [5] Banerjee, AK; Saha, PK, Pairwise semi bicompact and pairwise semi Lindeloff bispaces, Int. J. Math. Sci. Eng. Appl. (IJMSEA), 11, II, 47-56 (2017) [6] Banerjee, AK; Saha, PK, b*-open sets in bispaces, Int. J. Math. Stat. Invention (IJMSI), 4, 6, 39-43 (2016) [7] Banerjee, AK; Mondal, R., A note on discontinuity of mappings in a bispace, J. Cal. Math. Soc., 13, 2, 105-112 (2017) · Zbl 1400.54001 [8] Banerjee, AK; Pal, J., Semi λ*-closed sets and new separation axioms in Alexandroff spaces. South East Asian J. Math, Math. Sci., 14, 1, 115-134 (2018) [9] Banerjee, AK; Pal, J., λ*-closed sets and new separation axioms in Alexandraff spaces, Korean J. Math., 26, 4, 709-727 (2018) · Zbl 1428.54002 [10] Császár, A., Generalized open sets in generalized topologies, Acta Math. Hung., 106, 12, 53-66 (2005) · Zbl 1076.54500 [11] Das, P.; Rashid, MA, g*-closed sets and a new separation axioms in Alexandroff spaces, Archivum Mathematicum (BRNO), Tomus, 39, 299-307 (2003) [12] Dunham, W., T_1/2-spaces, Kyungpook Math. J., 17, 2, 161-169 (1977) · Zbl 0382.54013 [13] EI-Tantawy, OA; Abu-Donia, HM, Generalised separation axioms in bitopological spaces, Arab. J. Sci. Eng., 30, 1, 117-129 (2005) [14] Kelly, JC, Bitopological spaces, Proc. Lond. Math. Soc. (3), 13, 71-89 (1963) · Zbl 0107.16401 [15] Lahiri, BK; Das, P., Certain bitopological concepts in a bispace, Soochow J. Math., 27, 2, 175-185 (2001) · Zbl 0985.54028 [16] Levine, N., Generalised closed sets in topology, Rend. Cire. Mat. Palermo, 19, 2, 89-96 (1970) · Zbl 0231.54001 [17] Reilly, IL, On bitopological separation properties, Nanta Math., 5, 14-25 (1972) · Zbl 0245.54029 [18] Reilly, I.L.: On essential pairwise Hausdorff spaces. Serie II-tomo XXV, Anno, Rendiconti del circolo Mathematico Di Palermo, pp. 47-52 (1976) [19] Sarsak, MS, New separation axioms in generalized topological spaces, Acta Math. Hung., 132, 3, 244-252 (2011) · Zbl 1249.54007 [20] Tripathy, BC; Sarma, DJ, On b-locally open sets in bitopological spaces, Kyungpook Math. J., 51, 4, 429-433 (2011) · Zbl 1237.54030 [21] Tripathy, BC; Sarma, DJ, On weakly b-continuous functions in bitopological spaces, Acta Sci. Technol., 35, 3, 521-525 (2013) [22] Tripathy, BC; Sarma, DJ, Generalized b-closed sets in ideal bitopological spaces, Proyecciones J. Math., 33, 3, 315-324 (2014) · Zbl 1304.54056 [23] Tripathy, BC; Debnath, S., On fuzzy b-locally open sets in bitopological spaces, Songklanakarin J. Sci. Technol., 37, 1, 93-96 (2015) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.