Chattopadhyay, Chandan; Roy, Uttam Kumar \(\delta\)-sets, irresolvable and resolvable spaces. (English) Zbl 0752.54008 Math. Slovaca 42, No. 3, 371-378 (1992). A subset \(S\) of a topological space \(X\) is called by the authors a \(\delta\)-set, if \(\text{int cl }S\subseteq\text{cl int }S\), and the collection of all \(\delta\)-sets of \(X\) is denoted by \(T^ \delta\). In this paper the authors examine the relationships between the family \(T^ \delta\) and the properties of resolvability and irresolvability of the space in question (a space is resolvable if it admits two disjoint dense subsets, otherwise it is called irresolvable). In addition, a characterization of maximal resolvable spaces is provided. Reviewer: M.Ganster (Graz) Cited in 2 Documents MSC: 54D99 Fairly general properties of topological spaces 54E99 Topological spaces with richer structures Keywords:submaximal space; resolvability; irresolvability × Cite Format Result Cite Review PDF Full Text: EuDML References: [1] BAIRAGYA S. N., BAISNAB A. P.: On structure of generalized open sets. Bull. Calcutta Math. Soc. 79 (1987), 81-88. · Zbl 0645.54005 [2] CAMERON D. E.: Maximal and minimal topologies. Trans. Amer. Math. Soc. 160 (1971), 229-248. · Zbl 0202.22302 · doi:10.2307/1995802 [3] CAMERON D. E.: A class of maximal topologies. Pacific J. Math. 70 (1977), 101-104. · Zbl 0335.54022 · doi:10.2140/pjm.1977.70.101 [4] CHATTOPADHYAY C., BANDYOPADHYAY C.: On structure of \delta -sets. · Zbl 0764.54001 [5] GANSTER M., REILLY I. L., VAMANAMURTHY M. K.: Dense sets and irresolvable spaces. Ricerche Mat. XXXVI (1987). · Zbl 0698.54020 [6] GANSTER M.: Pre-open sets and resolvable spaces. Kyungpook Math. J. 27 (1987), 135-143. · Zbl 0665.54001 [7] HEWITT E.: A problem of set theoretic topology. Duke Math. J. 10 (1943), 309-333. · Zbl 0060.39407 · doi:10.1215/S0012-7094-43-01029-4 [8] LEVINE N.: Simple extensions of topologies. Amer. Math. Monthly 71 (1964), 22-25. · Zbl 0121.17203 · doi:10.2307/2311297 [9] NJASTAD O.: On some classes of nearly open sets. Pacific J. Math. 15 (1965), 961-970. · Zbl 0137.41903 · doi:10.2140/pjm.1965.15.961 [10] RAHA A. B.: Maximal topologies. J. Austral. Math. Soc. 15 (1973), 27. · Zbl 0267.54018 · doi:10.1017/S1446788700013197 [11] SMYTHE N., WILKINS C. A.: Minimal Hausdorff and maximal compact spaces. J. Austral. Math. Soc. 3 (1963), 167-171. · Zbl 0163.17201 · doi:10.1017/S1446788700027907 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.