Acta Mathematica Hungarica

, Volume 140, Issue 1–2, pp 47–59 | Cite as

On generalized cluster sets of functions and multifunctions



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.

Key words and phrases

(μi,μj)-adhere (μi,μj)-converge g-cluster set g-closedness (μ1μ2,η)-continuity 

Mathematics Subject Classification

54A05 54D20 54D30 54C60 54C99 


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2013

Authors and Affiliations

  1. 1.Department of MathematicsWest Bengal State UniversityKolkataIndia

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