g * -closed sets and a new separation axiom in Alexandroff spaces

Pratulananda Das; Md. Mamun Ar Rashid

Archivum Mathematicum (2003)

  • Volume: 039, Issue: 4, page 299-307
  • ISSN: 0044-8753

Abstract

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In this paper we introduce the concept of g * -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 * -closed sets and investigate some of its consequences.

How to cite

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Das, Pratulananda, and Rashid, Md. Mamun Ar. "$g^\ast $-closed sets and a new separation axiom in Alexandroff spaces." Archivum Mathematicum 039.4 (2003): 299-307. <http://eudml.org/doc/249140>.

@article{Das2003,
abstract = {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.},
author = {Das, Pratulananda, Rashid, Md. Mamun Ar},
journal = {Archivum Mathematicum},
keywords = {space; $g^\{\ast \}$-closed sets; $g^\{\ast \}$-open sets; $T_\{w\}$-space; generalized closed sets},
language = {eng},
number = {4},
pages = {299-307},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {$g^\ast $-closed sets and a new separation axiom in Alexandroff spaces},
url = {http://eudml.org/doc/249140},
volume = {039},
year = {2003},
}

TY - JOUR
AU - Das, Pratulananda
AU - Rashid, Md. Mamun Ar
TI - $g^\ast $-closed sets and a new separation axiom in Alexandroff spaces
JO - Archivum Mathematicum
PY - 2003
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 039
IS - 4
SP - 299
EP - 307
AB - 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.
LA - eng
KW - space; $g^{\ast }$-closed sets; $g^{\ast }$-open sets; $T_{w}$-space; generalized closed sets
UR - http://eudml.org/doc/249140
ER -

References

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  1. Alexandroff A. D., Additive set functions in abstract spaces, Mat. Sb. (N.S.) 8(50) (1940), 307–348 (English, Russian summary). (1940) Zbl0023.39701MR0004078
  2. Alexandroff A. D., Additive set functions in abstract spaces, Mat. Sb. (N.S.) 9(51) (1941), 563–628 (English, Russian summary). (1941) Zbl0028.07201MR0005785
  3. Das P., Samanta S. K., Pseudo-topological spaces, Sains Malaysiana, 21(4) (1992), 101–107. (1992) 
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  5. Das P., Rashid M. A., Certain separation axioms in a space, Korean J. Math. Sciences, 7(2000), 81–93. 
  6. Dunham W., T 1 / 2 -spaces, Kyungpook Math. J., 17(2) (1977), 161–169. (1977) MR0470934
  7. Dunham W., A new closure operator for not- T 1 -topologies, Kyungpook Math. J., 22 (1982), 55–60. (1982) MR0672085
  8. Lahiri B. K., Das P., Semi open sets in a space, Sains Malaysiana, 24(4) (1995), 1–11. (1995) 
  9. Lahiri B. K., Das P., Certain bitopological concepts in a bispace, Soochow J. of Math. 27(2) (2001), 175–185. Zbl0985.54028MR1838570
  10. Levine N., Generalized closed sets in topology, Rend. Circ. Mat. Palermo 19(2) (1970), 89–96. (19(2) MR0305341
  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. (1983) Zbl0511.54003MR0707797
  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. (1961) MR0148838

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