Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 51, No. 2, pp. 547-576 (2010)

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Compactness and boundedness of tangent spaces to metric spaces

O. Dovgoshey, F. Abdullayev and M. Küçükaslan

Institute of Applied Mathematics and Mechanics of NASU, R. Luxemburg str. 74, Donetsk 83114, Ukraine, e-mail:;

Mersin University, Faculty of Literature and Science, Department of Mathematics, 33342 Mersin, Turkey, e-mail:

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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Electronic version published on: 24 Jun 2010. This page was last modified: 8 Sep 2010.

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© 2010 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition