Characterization of ultra separation axioms via $(1,2)\alpha$-kernel
Lobachevskii journal of mathematics, Tome 25 (2007), pp. 217-229.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we introduce the concept of weakly-ultra-separation of two sets in a bitopological space using $(1,2)\alpha$-open sets. The $(1,2)\alpha$-closure and the $(1,2)\alpha$-kernel are defined in terms of this weakly-ultra-separation. We also investigate the properties of some weak separation axioms like ultra-$T_0$, ultra-$T_1$, and ultra-$R_0$.
Keywords: $(1,2)\alpha$-kernel and weakly-ultra-separated.
@article{LJM_2007_25_a6,
     author = {R. RajaRajeswari and M. L. Thivagar and S. A. Ponmani},
     title = {Characterization of ultra separation axioms via $(1,2)\alpha$-kernel},
     journal = {Lobachevskii journal of mathematics},
     pages = {217--229},
     publisher = {mathdoc},
     volume = {25},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2007_25_a6/}
}
TY  - JOUR
AU  - R. RajaRajeswari
AU  - M. L. Thivagar
AU  - S. A. Ponmani
TI  - Characterization of ultra separation axioms via $(1,2)\alpha$-kernel
JO  - Lobachevskii journal of mathematics
PY  - 2007
SP  - 217
EP  - 229
VL  - 25
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/LJM_2007_25_a6/
LA  - en
ID  - LJM_2007_25_a6
ER  - 
%0 Journal Article
%A R. RajaRajeswari
%A M. L. Thivagar
%A S. A. Ponmani
%T Characterization of ultra separation axioms via $(1,2)\alpha$-kernel
%J Lobachevskii journal of mathematics
%D 2007
%P 217-229
%V 25
%I mathdoc
%U http://geodesic.mathdoc.fr/item/LJM_2007_25_a6/
%G en
%F LJM_2007_25_a6
R. RajaRajeswari; M. L. Thivagar; S. A. Ponmani. Characterization of ultra separation axioms via $(1,2)\alpha$-kernel. Lobachevskii journal of mathematics, Tome 25 (2007), pp. 217-229. http://geodesic.mathdoc.fr/item/LJM_2007_25_a6/

[1] C. E. Aull and W. J. Thron, “Separation axioms between $T_0$ and $T_1$”, Indag. Math., 24 (1962), 26–37 | MR

[2] M. Caldas, “Semi-$T_{1/2}$ Spaces”, Pro. Math., 8 (1994), 115–121 | MR

[3] K. K. Dube and R. K. Sengai, “Semi-$T_D$ topological spaces”, UOU Report, 16:2 (1985), 307–310 | MR | Zbl

[4] K. K. Dube and B. N. Patel, “Semi-open sets with the axioms between $T_0$ and $T-1$”, Journal 06 Natural science, 3:1 (1993), 1–10

[5] S. Jafari, S. Athisaya Ponmani and Lellis Thivagar, M., “$(1,2)\alpha$-open sets based on bitopological separation properties”, Soochow. J. of Mathematics (to appear)

[6] J. C. Kelly, “Bitopological spaces”, Proc. London Math. Soc. (3), 13 (1963), 71–89 | DOI | MR | Zbl

[7] M. Lellis Thivagar, “Generalization of pairwise $\alpha$-continuous function”, Pure and Applied Mathematics and sciences, 33:1–2 (1991), 55–63 | MR | Zbl

[8] G. B. Navalagi, M. Lellis Thivagar, R. Raja Rajeswari and S. Athisya Ponmani, “A note on $(1,2)\alpha$-hyperconnected spaces”, International Journal of Mathematics and Analysis, 3 (2006), 121–129

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

[10] R. Raja Rajeswari and M. Lellis Thivagar, “On Bitopological ultra-spaces”, South East Asian Bulletin of Mathematics, 31 (2007) (to appear) | MR