On the gluing of hyperconvex metrics and diversities

Bożena Piątek

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica (2014)

  • Volume: 13, page 65-76
  • ISSN: 2300-133X

Abstract

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In this work we consider two hyperconvex diversities (or hyperconvex metric spaces) (X, δX) and (Y, δY ) 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.

How to cite

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Bożena Piątek. "On the gluing of hyperconvex metrics and diversities." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 13 (2014): 65-76. <http://eudml.org/doc/268795>.

@article{BożenaPiątek2014,
abstract = {In this work we consider two hyperconvex diversities (or hyperconvex metric spaces) (X, δX) and (Y, δY ) 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.},
author = {Bożena Piątek},
journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},
language = {eng},
pages = {65-76},
title = {On the gluing of hyperconvex metrics and diversities},
url = {http://eudml.org/doc/268795},
volume = {13},
year = {2014},
}

TY - JOUR
AU - Bożena Piątek
TI - On the gluing of hyperconvex metrics and diversities
JO - Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
PY - 2014
VL - 13
SP - 65
EP - 76
AB - In this work we consider two hyperconvex diversities (or hyperconvex metric spaces) (X, δX) and (Y, δY ) 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.
LA - eng
UR - http://eudml.org/doc/268795
ER -

References

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  2. [2] M. Bridson, A. Haefliger, Metric Spaces of Non-Positive Curvature, Grundlehren der Mathematischen Wissenschaften 319, Springer-Verlag, Berlin, 1999. Cited on 70. 
  3. [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.[WoS] 
  4. [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. 
  5. [5] R. Espínola, B. Piatek, Diversities, hyperconvexity and fixed points, Nonlinear Anal. 95 (2014), 229-245. Cited on 65, 66 and 67.[WoS] 
  6. [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. 
  7. [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. 
  8. [8] D. Faith, Conservation evaluation and phylogenetic diversity, Biol. Conserv. 61 (1992), 1-10. Cited on 65. 
  9. [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. 

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