In this paper, the characterization of Γ-convergence for the first countable topological spaces, characterization of convergence in supremum metric in general setting and some mutual relation between these convergences are discussed. The Γ-convergence is defined as the Kuratowaski-Painlevé convergence of the endographs of the intuitionistic fuzzy sets. The supremum metric is the supremum of Hausdroff distance among the η-cuts of the intuitionistic fuzzy sets. To study these convergences is an important part of the theoretical fundamentals for intuitionistic fuzzy set theory. Some results are given as an application to variational analysis.
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