Between closed sets and generalized closed sets in closure spaces
Communications in Mathematics, Tome 16 (2008) no. 1, pp. 3-14
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 54A05, 54D10
Keywords: closure operator; generalized closed set; $\partial $-closed set; $\partial $-continuous map
@article{COMIM_2008_16_1_a0,
     author = {Boonpok, Chawalit and Khampakdee, Jeeranunt},
     title = {Between closed sets and generalized closed sets in closure spaces},
     journal = {Communications in Mathematics},
     pages = {3--14},
     year = {2008},
     volume = {16},
     number = {1},
     mrnumber = {2498632},
     zbl = {1195.54002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/COMIM_2008_16_1_a0/}
}
TY  - JOUR
AU  - Boonpok, Chawalit
AU  - Khampakdee, Jeeranunt
TI  - Between closed sets and generalized closed sets in closure spaces
JO  - Communications in Mathematics
PY  - 2008
SP  - 3
EP  - 14
VL  - 16
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/COMIM_2008_16_1_a0/
LA  - en
ID  - COMIM_2008_16_1_a0
ER  - 
%0 Journal Article
%A Boonpok, Chawalit
%A Khampakdee, Jeeranunt
%T Between closed sets and generalized closed sets in closure spaces
%J Communications in Mathematics
%D 2008
%P 3-14
%V 16
%N 1
%U http://geodesic.mathdoc.fr/item/COMIM_2008_16_1_a0/
%G en
%F COMIM_2008_16_1_a0
Boonpok, Chawalit; Khampakdee, Jeeranunt. Between closed sets and generalized closed sets in closure spaces. Communications in Mathematics, Tome 16 (2008) no. 1, pp. 3-14. http://geodesic.mathdoc.fr/item/COMIM_2008_16_1_a0/

[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 | Zbl

[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

[3] Boonpok C.: Generalized closed sets in closure spaces. to appear. | Zbl

[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 | Zbl

[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 | Zbl

[7] Cueva M.C.: On g-closed sets and g-continuous mapping. Kyungpook Math. J., 33(1993), 205–209. | MR

[8] Gnanabal Y.: On generalized preregular closed sets in topological spaces. Indian J. Pure & Appl. Math., 28 (3) (1977), 351–360. | MR

[9] Levine N.: Semi-open sets and semi-continuity in topological spaces. Amer. Math. Monthly, 70 (1963), 36–41. | DOI | MR | Zbl

[10] Levine N.: Generalized closed sets in topology. Rend. Circ. Mat. Palermo, 19 (1970), 89–96. | DOI | MR | Zbl

[11] Maki H., Devi R., Balachandran K.: Generalized $\alpha$-closed sets in topology. Bull. Fukuoka Univ. Ed. Part III, 42 (1993), 13–21. | Zbl

[12] Njastad O.: On some classes of nearly open sets. Pacific J. Math. 15 (1965), 961–970. | DOI | MR | Zbl

[13] Palaniappan N., Rao K.C.: Regular generalized closed sets. Kyungpook Math. J., 33(1993), 211–219. | MR | Zbl

[14] Skula L.: Systeme von stetigen abbildungen, Czech. Math. J. 17 (92) (1967), 45–52. | MR

[15] Šlapal J.: Closure operations for digital topology. Theoret. Comput. Sci., 305 (2003), 457–471. | DOI | MR