A NEW TYPE OF CLUSTER SETS AND ITS APPLICATIONS

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Published: Dec 1, 1995
DOI: https://doi.org/10.5556/j.tkjm.26.1995.4413
Keywords:
delta-cluster set multifunction nearly compact space nearly Lindelof space almost regularity

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M. N. MUKHERJEE
Department of Pure Mathematics, University of Calcutta, 35-Ballygunge Circular Road, Calcutta-700 019, India.
S. RAYCHAUDHURI
Department of Pure Mathematics, University of Calcutta, 35-Ballygunge Circular Road, Calcutta-700 019, India.

Abstract




In this paper we introduce the concept of a new type of cluster sets, termed $\delta$-cluster sets, of functions and multifunctions between topological spaces. Expressions of such sets are found and multifunctions with $\delta$-closed graphs are characterized. Also the behaviour of $\delta$-cluster sets toward a-continuity of a func- tion is observed. Finally as applications, we find new characterizations of almost regularity, near compactness and near Lindelofness of a topological space in terms of $\delta$-cluster sets of suitable multifunctions.




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How to Cite
MUKHERJEE, M. N., & RAYCHAUDHURI, S. (1995). A NEW TYPE OF CLUSTER SETS AND ITS APPLICATIONS. Tamkang Journal of Mathematics, 26(4), 327–336. https://doi.org/10.5556/j.tkjm.26.1995.4413
Issue
Vol. 26 No. 4 (1995)
Section
Papers
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