| Title:
|
$g^\ast $-closed sets and a new separation axiom in Alexandroff spaces (English) |
| Author:
|
Das, Pratulananda |
| Author:
|
Rashid, Md. Mamun Ar |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
39 |
| Issue:
|
4 |
| Year:
|
2003 |
| Pages:
|
299-307 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we introduce the concept of $g^{\ast }$-closed sets and investigate some of its properties in the spaces considered by A. D. Alexandroff [1] where only countable unions of open sets are required to be open. We also introduce a new separation axiom called $T_{w}$-axiom in the Alexandroff spaces with the help of $g^{\ast }$-closed sets and investigate some of its consequences. (English) |
| Keyword:
|
space |
| Keyword:
|
$g^{\ast }$-closed sets |
| Keyword:
|
$g^{\ast }$-open sets |
| Keyword:
|
$T_{w}$-space |
| MSC:
|
54A05 |
| MSC:
|
54C08 |
| MSC:
|
54D10 |
| idZBL:
|
Zbl 1111.54001 |
| idMR:
|
MR2032103 |
| . |
| Date available:
|
2008-06-06T22:42:25Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107878 |
| . |
| Reference:
|
[1] Alexandroff A. D.: Additive set functions in abstract spaces.Mat. Sb. (N.S.) 8(50) (1940), 307–348 (English, Russian summary). Zbl 0023.39701, MR 0004078 |
| Reference:
|
[2] Alexandroff A. D.: Additive set functions in abstract spaces.Mat. Sb. (N.S.) 9(51) (1941), 563–628 (English, Russian summary). Zbl 0028.07201, MR 0005785 |
| Reference:
|
[3] Das P., Samanta S. K.: Pseudo-topological spaces.Sains Malaysiana, 21(4) (1992), 101–107. |
| Reference:
|
[4] Das P., Rashid M. A.: Semi-closed sets in a space.Bull. Gauhati Univ. Math. Ass., 6(1999), 27–36. |
| Reference:
|
[5] Das P., Rashid M. A.: Certain separation axioms in a space.Korean J. Math. Sciences, 7(2000), 81–93. |
| Reference:
|
[6] Dunham W.: $T_{1/2}$-spaces.Kyungpook Math. J., 17(2) (1977), 161–169. MR 0470934 |
| Reference:
|
[7] Dunham W.: A new closure operator for not-$T_{1}$-topologies.Kyungpook Math. J., 22 (1982), 55–60. MR 0672085 |
| Reference:
|
[8] Lahiri B. K., Das P.: Semi open sets in a space.Sains Malaysiana, 24(4) (1995), 1–11. |
| Reference:
|
[9] Lahiri B. K., Das P.: Certain bitopological concepts in a bispace.Soochow J. of Math. 27(2) (2001), 175–185. Zbl 0985.54028, MR 1838570 |
| Reference:
|
[10] Levine N.: Generalized closed sets in topology.Rend. Circ. Mat. Palermo 19(2) (1970), 89–96. MR 0305341 |
| Reference:
|
[11] Mashhour A. S., Allam A. A., Mahmoud A. A., Khedr F. H.: On supratopological spaces.Indian J. Pure Appl. Math. 14(4) (1983), 502–510. Zbl 0511.54003, MR 0707797 |
| Reference:
|
[12] Varadarajan V. S.: Measures on topological spaces.(Russian), Mat. Sb. (N.S.) 55(97) 1961, 33–100, Amer. Math. Soc. Translations, 78(2) (1965), 161–228. MR 0148838 |
| . |
