## Missouri Journal of Mathematical Sciences

### A New Kind of Cluster Sets and Their Applications

#### Abstract

In this article, we introduce $s$-cluster sets of functions and multifunctions and investigate their various properties. Such investigations provide a new technique for studying $s$-closed spaces [7] and weakly Hausdorff spaces [9].

#### Article information

Source
Missouri J. Math. Sci., Volume 21, Issue 3 (2009), 198-205.

Dates
First available in Project Euclid: 14 September 2011

https://projecteuclid.org/euclid.mjms/1316024885

Digital Object Identifier
doi:10.35834/mjms/1316024885

Mathematical Reviews number (MathSciNet)
MR2584545

Zentralblatt MATH identifier
1182.54027

#### Citation

Basu, C. K.; Ghosh, M. K. A New Kind of Cluster Sets and Their Applications. Missouri J. Math. Sci. 21 (2009), no. 3, 198--205. doi:10.35834/mjms/1316024885. https://projecteuclid.org/euclid.mjms/1316024885

#### References

• E. F. Collingwood and A. J. Lohwater, The Theory of Cluster Sets, Cambridge University Press, Cambridge, 1966.
• S. G. Crossely and S. K. Hildebrand, Semi-closure, Texas J. of Science, 22 (1971), 99–112.
• T. R. Hamlett, Applications of Cluster Sets in Minimal Topological Spaces, Proc. Amer. Math. Soc., 53 (1975), 477–480.
• T. R. Hamlett, Cluster Sets in General Topology, J. London Math. Soc., 12 (1976), 192–198.
• J. E. Joseph, Multifunctions and Cluster Sets, Proc. Amer. Math. Soc., 74 (1979), no. 2, 329–337.
• N. Levine, Semi-open Sets and Semi-continuity in Topological Spaces, Amer. Math. Monthly, 70 (1963), 54–61.
• G. D. Maio and T. Noiri, On $s$-closed Spaces, Indian J. Pure and Appl. Math., 18 (1987), 226–233.
• M. N. Mukherjee and A. Debray, On $S$-cluster Sets and $S$-closed Spaces, Internat. J. Math. and Math. Sci., 23 (2000), 597–603.
• T. Soundararajan, General Topology and its Relations to Modern Analysis and Algebra III, Proc. Conf. Kanpur, 1968, Academica, Prague, (1971), 301–306.
• W. J. Thron, Proximity Structure and Grills, Math. Ann., 206 (1973), 35–62.
• N. V. Veličko, H-closed Toplogical Spaces, Amer. Math. Soc. Transl., 78 (1968), 103–118.
• J. D. Weston, Some Theorems on Cluster Sets, J. London Math. Soc., 33 (1958), 435–441.