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On generalized cluster sets of functions and multifunctions
R. Bhowmick,
Published in
Volume: 140
Issue: 1-2
Pages: 47 - 59
This paper introduces and studies generalized cluster sets (g-cluster sets) of functions and multifunctions on GTS, which unifies the existing notions of cluster sets, θ-cluster sets, δ-cluster sets, S-cluster sets, s-cluster sets, p-cluster sets and many more. Several properties of the functions and multifunctions as well as their range and domain spaces are observed via degeneracies of their g-cluster sets. Characterizations of g-cluster sets through filterbases and grills on a typical class of GTS's are also obtained. Moreover, μ-compactness of a GTS is characterized through g-cluster sets of multifunctions. © 2013 Akadémiai Kiadó, Budapest, Hungary.
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JournalActa Mathematica Hungarica