Tripathy, Binod Chandra; Ray, Gautam Chandra Fuzzy \(\delta^\ast \)-almost continuous and fuzzy \(\delta^\ast \)-continuous functions in mixed fuzzy ideal topological spaces. (English) Zbl 1455.54011 Proyecciones 39, No. 2, 435-449 (2020). Summary: In this paper we introduce two new classes of functions between mixed fuzzy topological spaces, namely fuzzy \(\delta^\ast \)-almost continuous and fuzzy \(\delta^\ast \)-continuous functions and investigate some of their properties. The description of these two types of functions is facilitated by the introduction of generalized open sets, called fuzzy \(\delta \)-preopen sets, fuzzy \(\delta \)-precluster point, fuzzy preopen sets, fuzzy \(\delta \)-pre-\(q\)-neighbourhoods. Cited in 7 Documents MSC: 54A40 Fuzzy topology 54D20 Noncompact covering properties (paracompact, Lindelöf, etc.) 54C08 Weak and generalized continuity 54C10 Special maps on topological spaces (open, closed, perfect, etc.) 54A05 Topological spaces and generalizations (closure spaces, etc.) 54C60 Set-valued maps in general topology 54E55 Bitopologies Keywords:fuzzy \(\delta \)-preopen set; fuzzy \(\delta \)-regular open set; fuzzy \(\delta \)-pre neighbourhood; fuzzy \(\delta \)-regular neighbourhood PDFBibTeX XMLCite \textit{B. C. Tripathy} and \textit{G. C. Ray}, Proyecciones 39, No. 2, 435--449 (2020; Zbl 1455.54011) Full Text: DOI References: [1] A. Alexiewicz and Z. Semadeni, “A generalization of two norm spaces”,Bulletin of the Polish Academy of Sciences Mathematics, vol. 6, pp. 135-139, 1958. · Zbl 0082.10902 [2] C. I. Chang, “Fuzzy topological spaces”,Journal of mathematical analysis and applications, vol. 24, no. 1, pp. 182-190, Oct. 1968, doi: 10.1016/0022-247x(68)90057-7. [3] A. Chilana, “The space of bounded sequences with the mixed topology”,Pacific journal of mathematics, vol. 48, no. 1, pp. 29-33, Sep. 1973, doi: 10.2140/pjm.1973.48.29. · Zbl 0247.46025 [4] J. B. Cooper, “The strict topology and spaces with mixed topologies”,Proceedings of the American Mathematical Society, vol. 30, no. 3, pp. 583-583, Nov. 1971, doi: 10.1090/s0002-9939-1971-0284789-2. · Zbl 0225.46004 [5] J. B. Cooper, “The Mackey topology as a mixed topology”,Proceedings of the American Mathematical Society , vol. 53, no. 1, pp. 107-112, Jan. 1975, doi: 10.1090/s0002-9939-1975-0383059-5. · Zbl 0321.46003 [6] N. R. Das and P. B. Baishya, “Mixed fuzzy topological spaces”, Journal of fuzzy mathematics, vol. 3, no. 4, pp. 777-784, 1995. · Zbl 0870.54005 [7] M. Ganster, D. N. Georgiou, S. Jafari, and S. P. Moshokoa, “On some applications of fuzzy points”,Applied general topology, vol. 6, no. 2, pp. 119-133, Oct. 2005, doi: 10.4995/agt.2005.1951. · Zbl 1097.54007 [8] S. Ganguly and D. Singha, “Mixed topology for a bi-topological spaces”, Bulletin of the Calcutta Mathematical Society , vol. 76, pp. 304-314, 1984. [9] S. Ganguly and S. Saha, “A note on δ-continuity and δ-connected sets in fuzzy set theory”, Simon Stevin, vol. 62, pp. 127-141, 1988. · Zbl 0695.54008 [10] M. Alam and V. D. Esteruch, “A contribution to fuzzy subspaces”, Applied general topology , vol. 1, no. 3, pp. 13-23, 2002. [On line]. Available: https://bit.ly/3f0G8sl [11] K. Shravan and B. C. Tripathy, “Multiset mixed topological space”,Soft computing, vol. 23, no. 20, pp. 9801-9805, Feb. 2019, doi: 10.1007/s00500-019-03831-9. · Zbl 1430.54011 [12] B. C. Tripathyand G. C. Ray, “On mixed fuzzy topological spaces and countability”,Soft computing , vol. 16, no. 10, pp. 1691-1695, May 2012, doi: 10.1007/s00500-012-0853-1. · Zbl 1270.54012 [13] B. C. Tripathy and G. C. Ray , “Mixed fuzzy ideal topological spaces”,Applied mathematics and computation, vol. 220, pp. 602-607, Sep. 2013 doi: 10.1016/j.amc.2013.05.072. · Zbl 1330.54017 [14] B. C. Tripathyand G. C. Ray , “On δ-continuity in mixed fuzzy topological spaces”,Boletim da Sociedade Paranaense de matemática, vol. 32, no. 2, pp. 175-187, Sep. 2014, doi: 10.5269/bspm.v32i2.20254. [15] R. H. Warren, “Neighborhoods, bases and continuity in fuzzy topological spaces”,Rocky mountain journal of mathematics, vol. 8, no. 3, pp. 459-470, Sep. 1978, doi: 10.1216/rmj-1978-8-3-459. · Zbl 0394.54003 [16] A. Wiweger, “Linear spaces with mixed topology”,Studia mathematica, vol. 20, no. 1, pp. 47-68, 1961, doi: 10.4064/sm-20-1-47-68. · Zbl 0097.31301 [17] L. A. Zadeh, “Fuzzy sets”,Information and control, vol. 8, no. 3, pp. 338-353, Jun. 1965, doi: 10.1016/s0019-9958(65)90241-x. · Zbl 0139.24606 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.