Ekici, Erdal A new approach in topology via elements of an ideal. (English) Zbl 1430.54002 Acta Comment. Univ. Tartu. Math. 23, No. 1, 87-94 (2019). Summary: New approaches in topology or related branches of mathematics have contributed in a valuable way to the science, and have yielded various new topics for investigation. The main goal of this paper is to examine a new approach and so a new form of open sets via elements of an ideal. The concept of \(\alpha^\star_I \)-open sets is introduced and discussed. Cited in 1 Document MSC: 54A05 Topological spaces and generalizations (closure spaces, etc.) 54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) Keywords:\( \alpha_I^\star\)-open; \( \alpha \)-open; \( \alpha^\star_I \)-closed; ideal; \( \alpha\)-\(I\)-open; \(\star\)-dense; \(\star\)-continuous PDFBibTeX XMLCite \textit{E. Ekici}, Acta Comment. Univ. Tartu. Math. 23, No. 1, 87--94 (2019; Zbl 1430.54002) Full Text: DOI References: [1] ´A. Cs´asz´ar, Generalized open sets in generalized topologies, Acta Math. Hungar. 106 (2005), 53-66. · Zbl 1076.54500 [2] J. Dontchev, Idealization of Ganster-Reilly decomposition theorems, arxiv:math. GN/9901017v1, 1999. [3] J. Dontchev, M. Ganster, and D. Rose, Ideal resolvability, Topology Appl. 93 (1999), 1-16. · Zbl 0955.54001 [4] E. Ekici, Almost nearly continuous multifunctions, Acta Math. Univ. Comenian. 73(2) (2004), 175-186. · Zbl 1100.54008 [5] E. Ekici, On γ-Urysohn spaces, Adv. Stud. Contemp. Math. 11(2) (2005), 219-226. · Zbl 1081.54522 [6] E. Ekici, On C∗-sets and decompositions of continuous and ηζ-continuous functions, Acta Math. Hungar. 117(4) (2007), 325-333. · Zbl 1164.54322 [7] E. Ekici, Generalization of weakly clopen and strongly θ-b-continuous functions, Chaos Solitons Fractals 38 (2008), 79-88. · Zbl 1142.54330 [8] E. Ekici, Generalized hyperconnectedness, Acta Math. Hungar. 133(1-2) (2011), 140- 147. · Zbl 1249.54003 [9] E. Ekici, On R-I-open sets and A∗I-sets in ideal topological spaces, An. Univ. Craiova Ser. Mat. Inform. 38(2) (2011), 26-31. · Zbl 1249.54004 [10] E. Ekici, On weak structures due to Cs´asz´ar, Acta Math. Hungar. 134(4) (2012), 565-570. · Zbl 1265.54008 [11] E. Ekici, Further new generalized topologies via mixed constructions due to Cs´asz´ar, Math. Bohem. 140(1) (2015), 1-9. · Zbl 1349.54003 [12] E. Ekici and T. Noiri, Decompositions of continuity, α-continuity and AB-continuity, Chaos Solitons Fractals 41 (2009), 2055-2061. · Zbl 1198.54035 [13] E. Ekici and T. Noiri, ?-extremally disconnected ideal topological spaces, Acta Math. Hungar. 122(1-2) (2009), 81-90. · Zbl 1199.54006 [14] E. Ekici and J. H. Park, On weakly s-precontinuous multifunctions, Arab. J. Sci. Eng. Sect. A Sci. 32(1A) (2007), 83-92. · Zbl 1184.54017 [15] E. Hatir and T. Noiri, On decompositions of continuity via idealization, Acta Math. Hungar. 96 (2002), 341-349. · Zbl 1012.54019 [16] D. Jankovi´c and T. R. Hamlett, New topologies from old via ideals, Amer. Math. Monthly 97 (1990), 295-310. · Zbl 0723.54005 [17] K. Kuratowski, Topology, Vol. 1, Academic Press, New York, 1966. [18] S. Modak and T. Noiri, Remarks on locally closed set, Acta Comment. Univ. Tartu. Math. 22(1) (2018), 57-64. · Zbl 1400.54003 [19] T. Noiri and V. Popa, Minimal structures, punctually m-open functions in the sense of Kuratowski and bitopological spaces, Math. Commun. 12(2) (2007), 247-253. · Zbl 1151.54003 [20] S. Y¨uksel, A. A¸cikg¨oz, and T. Noiri, On δ-I-continuous functions, Turk J. Math. 29 (2005), 39-51. · Zbl 1064.54026 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.