Open AccessA NEW TYPE OF CLUSTER SETS AND ITS APPLICATIONS
Author(s) -
M. Mukherjee,
Subhadip Raychaudhuri
Publication year - 1995
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.26.1995.4413
Subject(s) - mathematics , compact space , cluster (spacecraft) , type (biology) , topological space , space (punctuation) , set (abstract data type) , topology (electrical circuits) , pure mathematics , combinatorics , computer science , ecology , biology , programming language , operating system
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.