Abstract
A criterion for the ultrametricity of pretangent spaces to general metric spaces is obtained.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. Heinonen, Lectures on Analysis on Metric Spaces. Universitext (Springer-Verlag, New York, 2001).
L. Ambrosio, “Metric space valued functions of bounded variation,” Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 17(3), 439–478 (1990).
L. Ambrosio, “Fine properties of sets of finite perimeter in doubling metric measure spaces,” Set-Valued Anal. 10(2–3), 111–128 (2002).
L. Ambrosio and B. Kircheim, “Currents in metric spaces,” Acta Math. 185(1), 1–80 (2000).
L. Ambrosio and B. Kircheim, “Rectifiable sets in metric and Banach spaces,” Math. Ann. 318(3), 527–555 (2000).
P. Hajłasz, “Sobolev spaces on an arbitrary metric space,” Potential Anal. 5(4), 403–415 (1996).
J. Cheeger, “Differentiability of Lipschitz functions on metric measure spaces,” Geom. Funct. Anal. 9(3), 428–517 (1999).
N. Shanmugalingam, “Newtonian space: an extension of Sobolev spaces to metric measure spaces,” Rev. Mat. Iberoamericana 16(2), 243–279 (2000).
M. Bridson and A. Haefliger, Metric Spaces of Non-Positive Curvature, in Grundlehren Math. Wiss. (Springer-Verlag, Berlin, 1999), Vol. 319.
O. Dovgoshey and O. Martio, Tangent Spaces to Metric Spaces, Preprint No. 480 (University of Helsinki, 2008).
O. Dovgoshey, F. Abdullayev, and M. Küçükaslan, “Compactness and boundedness of tangent spaces to metric spaces,” Beiträge Algebra Geom. 51(2), 547–576 (2010).
F. Abdullayev, O. Dovgoshey, and M. Küçükaslan, “Metric spaces with unique pretangent spaces. Conditions of the uniqueness,” Ann. Acad. Sci. Fenn.Math. 36(2), 353–392 (2011).
O. A. Dovgoshey, “Tangent spaces to metric spaces and to their subspaces,” Ukr. Math. Bull. 5(4), 459–477 (2008).
J. L. Kelley, General Topology, 2nd ed. (Springer, New York-Heidelberg-Berlin, 1975; Nauka, Moscow, 1968).
A. A. Dovgoshei and D. V. Dordovskii, “Ultrametricity of tangent spaces to metric spaces,” Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky, No. 3, 19–23 (2010).
O. Dovgoshey and D. Dordovskyi, “Ultrametricity and metric betweenness in tangent spaces to metric spaces,” p-Adic Numbers Ultrametric Anal. Appl. 2(2), 100–113 (2010).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A. A. Dovgoshei, D. V. Dordovskii, 2012, published in Matematicheskie Zametki, 2012, Vol. 92, No. 1, pp. 49–58.
Rights and permissions
About this article
Cite this article
Dovgoshei, A.A., Dordovskii, D.V. An ultrametricity condition for pretangent spaces. Math Notes 92, 43–50 (2012). https://doi.org/10.1134/S000143461207005X
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S000143461207005X