Acta Mathematica Hungarica

, Volume 140, Issue 1, pp 47–59

On generalized cluster sets of functions and multifunctions


DOI: 10.1007/s10474-013-0310-3

Cite this article as:
Bhowmick, R. & Deb Ray, A. Acta Math Hung (2013) 140: 47. doi:10.1007/s10474-013-0310-3


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)-convergeg-cluster setg-closedness(μ1μ2,η)-continuity

Mathematics Subject Classification


Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2013

Authors and Affiliations

  1. 1.Department of MathematicsWest Bengal State UniversityKolkataIndia