| Title:
|
Between closed sets and generalized closed sets in closure spaces (English) |
| Author:
|
Boonpok, Chawalit |
| Author:
|
Khampakdee, Jeeranunt |
| Language:
|
English |
| Journal:
|
Acta Mathematica Universitatis Ostraviensis |
| ISSN:
|
1214-8148 |
| Volume:
|
16 |
| Issue:
|
1 |
| Year:
|
2008 |
| Pages:
|
3-14 |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
closure operator |
| Keyword:
|
generalized closed set |
| Keyword:
|
$\partial $-closed set |
| Keyword:
|
$\partial $-continuous map |
| MSC:
|
54A05 |
| MSC:
|
54D10 |
| idZBL:
|
Zbl 1195.54002 |
| idMR:
|
MR2498632 |
| . |
| Date available:
|
2009-12-29T09:23:10Z |
| Last updated:
|
2013-10-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/137494 |
| . |
| Reference:
|
[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. Zbl 0923.54015, MR 1684940 |
| Reference:
|
[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 |
| Reference:
|
[3] Boonpok C.: Generalized closed sets in closure spaces., to appear. Zbl 1194.54004 |
| Reference:
|
[4] Čech E.: Topological Spaces., Topological Papers of Eduard Čech, Academia, Prague 1968, 436–472. |
| Reference:
|
[5] Chvalina J.: On homeomorphic topologies and equivalent set-systems., Arch. Math. 2, Scripta Fac. Sci. Nat. UJEP Brunensis, XII (1976), 107–116. Zbl 0349.54002, MR 0438267 |
| Reference:
|
[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. Zbl 0478.54001, MR 0673249 |
| Reference:
|
[7] Cueva M.C.: On g-closed sets and g-continuous mapping., Kyungpook Math. J., 33(1993), 205–209. MR 1253672 |
| Reference:
|
[8] Gnanabal Y.: On generalized preregular closed sets in topological spaces., Indian J. Pure & Appl. Math., 28 (3) (1977), 351–360. MR 1442845 |
| Reference:
|
[9] Levine N.: Semi-open sets and semi-continuity in topological spaces., Amer. Math. Monthly, 70 (1963), 36–41. Zbl 0113.16304, MR 0166752, 10.2307/2312781 |
| Reference:
|
[10] Levine N.: Generalized closed sets in topology., Rend. Circ. Mat. Palermo, 19 (1970), 89–96. Zbl 0231.54001, MR 0305341, 10.1007/BF02843888 |
| Reference:
|
[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 |
| Reference:
|
[12] Njastad O.: On some classes of nearly open sets., Pacific J. Math. 15 (1965), 961–970. Zbl 0137.41903, MR 0195040, 10.2140/pjm.1965.15.961 |
| Reference:
|
[13] Palaniappan N., Rao K.C.: Regular generalized closed sets., Kyungpook Math. J., 33(1993), 211–219. Zbl 0794.54002, MR 1253673 |
| Reference:
|
[14] Skula L.: Systeme von stetigen abbildungen, Czech. Math. J., 17 (92) (1967), 45–52. MR 0206917 |
| Reference:
|
[15] Šlapal J.: Closure operations for digital topology., Theoret. Comput. Sci., 305 (2003), 457–471. MR 2013581, 10.1016/S0304-3975(02)00708-9 |
| . |
