On the gluing of hyperconvex metrics and diversities

Bożena Piątek

doi:10.2478/aupcsm-2014-0006

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On the gluing of hyperconvex metrics and diversities

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Volume 13 (2014): Issue 1 (December 2014)

By: Bożena Piątek

Open Access

|Dec 2014

Abstract

In this work we consider two hyperconvex diversities (or hyperconvex metric spaces) (X, δ_X) and (Y, δ_Y ) with nonempty intersection and we wonder whether there is a natural way to glue them so that the new glued diversity (or metric space) remains being hyperconvex. We provide positive and negative answers in both situations.

References

[1] N. Aronszajn, P. Panitchpakdi, Extensions of uniformly continuous transformations and hyperconvex metric spaces, Pacific J. Math. 6 (1956), 405-439. Cited on 66 and 75.
Search in Google Scholar
[2] M. Bridson, A. Haefliger, Metric Spaces of Non-Positive Curvature, Grundlehren der Mathematischen Wissenschaften 319, Springer-Verlag, Berlin, 1999. Cited on 70.
Search in Google Scholar
[3] D. Bryant, P.F. Tupper, Hyperconvexity and tight-span theory for diversities, Adv. Math. 231 (2012), no. 6, 3172-3198. Cited on 65, 66, 67, 71 and 74.
Search in Google Scholar
[4] A.W.M. Dress, Trees, tight extensions of metric spaces, and the cohomological dimension of certain groups: a note on combinatorial properties of metric spaces, Adv. in Math. 53 (1984), no. 3, 321-402. Cited on 65.
Search in Google Scholar
[5] R. Espínola, B. Piatek, Diversities, hyperconvexity and fixed points, Nonlinear Anal. 95 (2014), 229-245. Cited on 65, 66 and 67.
Search in Google Scholar
[6] R. Espínola, A. Fernández León, Fixed Point Theory in Hyperconvex Metric Spaces, Topics in Fixed Point Theory, 101-158, Springer, Berlin, 2013. Cited on 66 and 71.
Search in Google Scholar
[7] R. Espínola, M.A. Khamsi, Introduction to hyperconvex spaces, Handbook of metric fixed point theory, 391-435, Kluwer Acad. Publ., Dordrecht, 2001. Cited on 66, 71, 74 and 75.
Search in Google Scholar
[8] D. Faith, Conservation evaluation and phylogenetic diversity, Biol. Conserv. 61 (1992), 1-10. Cited on 65.
Search in Google Scholar
[9] J.R Isbell, Injective envelopes of Banach spaces are rigidly attached, Bull. Amer. Math. Soc. 70 (1964), 727-729. Cited on 65 and 74.
Search in Google Scholar

Articles in this issue

DOI: https://doi.org/10.2478/aupcsm-2014-0006 | Journal eISSN: 2300-133X | Journal ISSN: 2081-545X

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Language: English

Page range: 65 - 76

Submitted on: Mar 22, 2014

Published on: Dec 11, 2014

Published by: Pedagogical University of Cracow

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Related subjects:

Mathematics,

General mathematics

© 2014 Bożena Piątek, published by Pedagogical University of Cracow
This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 License.

Volume 13 (2014): Issue 1 (December 2014)