Compactness and boundedness of tangent spaces to metric spaces

O. Dovgoshey, F. Abdullayev and M. Küçükaslan

Mersin University, Faculty of Literature and Science, Department of Mathematics, 33342 Mersin, Turkey, e-mail: fabdul@mersin.edu.tr mkucukaslan@mersin.edu.tr

Abstract: We describe metric spaces with bounded pretangent spaces and characterize proper metric spaces with proper tangent spaces. We also present the necessary and sufficient conditions under which a tangent space is compact and build a compact ultrametric space $X$ such that some pretangent space to $X$ has the density $\frak c$.

Keywords: metric spaces, tangent spaces to metric spaces, compact tangent spaces, bounded tangent spaces, proper tangent spaces

Classification (MSC2000): 54E35

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