STAR OPERATORS ON sn-NETWORKS

• Lin, Shou (Institute of Mathematics Ningde Teachers' College) ;
• Zhang, Jinhuang (Department of Mathematics and Information Science Zhangzhou Normal University)
• Published : 2012.07.31

Abstract

Star operations are defined by R. E. Hodel in 1994. In this paper some relations among star operators, sequential closure operators and closure operators are discussed. Moreover, we introduce an induced topology by a family of subsets of a space, and some interesting results about star operators are established by the induced topology.

Acknowledgement

Supported by : NSFC

References

1. A. V. Arhangel'skii, Mappings and spaces, Russian Math. Surveys 21 (1966), no. 4, 115-162.
2. A. V. Arhangel'skii and S. Franklin, Ordinal invariants for topological spaces, Michigan Math. J. 15 (1968), 313-320. https://doi.org/10.1307/mmj/1029000034
3. A. V. Arhangel'skii and L. S. Pontryagin, General Topology I, Springer-Verlage EMS 17, 1990.
4. R. Engelking, General Topology, (revised and completed edition), Berlin: Heldermann Verlag, 1989.
5. R. E. Hodel, ${\kappa}$-structures and topology, Papers on general topology and applications (Flushing, NY, 1992), 50-63, Ann. New York Acad. Sci., 728, New York Acad. Sci., New York, 1994. https://doi.org/10.1111/j.1749-6632.1994.tb44133.x
6. W. C. Hong, A note on weakly first countable spaces, Commun. Korean Math. Soc. 17 (2002), no. 3, 531-534. https://doi.org/10.4134/CKMS.2002.17.3.531
7. L. Shou, On sequence-covering s-mappings, Adv. Math. (China) 25 (1996), 548-551.
8. L. Shou, Point-countable Covers and Sequence-covering Mappings, Beijing: China Science Press, 2002.
9. F. Siwiec, On defining a space by a weak base, Pacific J. Math. 52 (1974), 133-145.