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2014 | 13 |

Tytuł artykułu

On the gluing of hyperconvex metrics and diversities

Autorzy

Treść / Zawartość

Języki publikacji

EN

Abstrakty

EN
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.

Rocznik

Tom

13

Daty

wydano
2014-12-01
otrzymano
2014-03-22
poprawiono
2014-06-23
online
2014-12-11

Twórcy

  • Institute of Mathematics Silesian University of Technology 44-100 Gliwice Poland

Bibliografia

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

Identyfikatory

Identyfikator YADDA

bwmeta1.element.doi-10_2478_aupcsm-2014-0006