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Some Remarks on Completeness and Compactness in G-Metric Spaces

Complete metric spaces have great importance in functional analysis and its applications. The purpose of this paper is to introduce and study on some types of completeness in generalized metric spaces by the aid of Bourbaki Cauchy and cofinally Bourbaki-Cauchy sequences which are belonging to the class bigger than the class of Cauchy sequences. Moreover, by transporting some topological concepts to generalized metric spaces, the relations between these concepts and these new types of completeness properties are given.