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Keywords:
closure operator; generalized closed set; $\partial $-closed set; $\partial $-continuous map
closure operator; generalized closed set; $\partial $-closed set; $\partial $-continuous map
Summary:
The purpose of the present paper is to define and study $\partial $-closed sets in closure spaces obtained as generalization of the usual closed sets. We introduce the concepts of $\partial $-continuous and $\partial $-closed maps by using $\partial $-closed sets and investigate some of their properties.
References:
[1] Arokiarani I., Balachandran K., Dontchev J.: Some characterizations of gp-irresolute and gp-continuous maps between topological spaces. Mem. Fac. Sci. Kochi Univ. Ser. A Math., 20 (1999), 93–104. MR 1684940 | Zbl 0923.54015
[2] Balachandran K., Sundaram P., Maki H.: On generalized continuous maps maps in topological spaces. Mem. Fac. Sci. Kochi Univ. Ser. A Math., 12 (1991), 5–13. MR 1093540
[3] Boonpok C.: Generalized closed sets in closure spaces. to appear. Zbl 1194.54004
[4] Čech E.: Topological Spaces. Topological Papers of Eduard Čech, Academia, Prague 1968, 436–472.
[5] Chvalina J.: On homeomorphic topologies and equivalent set-systems. Arch. Math. 2, Scripta Fac. Sci. Nat. UJEP Brunensis, XII (1976), 107–116. MR 0438267 | Zbl 0349.54002
[6] Chvalina J.: Stackbases in power sets of neighbourhood spaces preserving the continuity of mappings. Arch. Math. 2, Scripta Fac. Sci. Nat. UJEP Brunensis, XVII (1981), 81–86. MR 0673249 | Zbl 0478.54001
[7] Cueva M.C.: On g-closed sets and g-continuous mapping. Kyungpook Math. J., 33(1993), 205–209. MR 1253672
[8] Gnanabal Y.: On generalized preregular closed sets in topological spaces. Indian J. Pure & Appl. Math., 28 (3) (1977), 351–360. MR 1442845
[9] Levine N.: Semi-open sets and semi-continuity in topological spaces. Amer. Math. Monthly, 70 (1963), 36–41. DOI 10.2307/2312781 | MR 0166752 | Zbl 0113.16304
[10] Levine N.: Generalized closed sets in topology. Rend. Circ. Mat. Palermo, 19 (1970), 89–96. DOI 10.1007/BF02843888 | MR 0305341 | Zbl 0231.54001
[11] Maki H., Devi R., Balachandran K.: Generalized $\alpha$-closed sets in topology. Bull. Fukuoka Univ. Ed. Part III, 42 (1993), 13–21. Zbl 0888.54005
[12] Njastad O.: On some classes of nearly open sets. Pacific J. Math. 15 (1965), 961–970. DOI 10.2140/pjm.1965.15.961 | MR 0195040 | Zbl 0137.41903
[13] Palaniappan N., Rao K.C.: Regular generalized closed sets. Kyungpook Math. J., 33(1993), 211–219. MR 1253673 | Zbl 0794.54002
[14] Skula L.: Systeme von stetigen abbildungen, Czech. Math. J. 17 (92) (1967), 45–52. MR 0206917
[15] Šlapal J.: Closure operations for digital topology. Theoret. Comput. Sci., 305 (2003), 457–471. DOI 10.1016/S0304-3975(02)00708-9 | MR 2013581
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