On the gluing of hyperconvex metrics and diversities

Bożena Piątek


In this work we consider two hyperconvex diversities (or hyperconvex metric spaces) (X; dX) and (Y; dY ) with nonempty intersection are given 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.


Gluing of spaces; Hyperconvexity; Diversity

Mathematics Subject Classification (2010)



Aronszajn, N. and P. Panitchpakdi. "Extensions of uniformly continuous transformations and hyperconvex metric spaces." Pacific J. Math. 6 (1956): 405-439.

Bridson, M. and A. Haefliger. "Metric Spaces of Non-Positive Curvature" Springer-Verlag, Berlin: Grundlehren der Mathematischen Wissenschaften 319, 1999.

Bryant, D. and P.F. Tupper. "Hyperconvexity and tight-span theory for diversities." Adv. Math. 231.6 (2012): 3172-3198.

Dress, A.W.M. "Trees, tight extensions of metric spaces, and the cohomological dimension of certain groups: a note on combinatorial properties of metric spaces." Adv. in Math. 53.3 (1984): 321-402.

Espínola, R. and B. Piatek "Diversities, hyperconvexity and fixed points." Nonlinear Anal. 95 (2014): 229-245.

Espínola, R. and A. Fernández León. "Fixed Point Theory in Hyperconvex Metric Spaces." Springer, Berlin: Topics in Fixed Point Theory, 101-158, 2013.

Espínola, R. and M.A. Khamsi. "Introduction to hyperconvex spaces, Handbook of metric fixed point theory." 391–435. Dordrecht: Kluwer Acad. Publ., 2001.

Faith, D. "Conservation evaluation and phylogenetic diversity." Biol. Conserv. 61 (1992): 1-10.

Isbell, J.R. "Injective envelopes of Banach spaces are rigidly attached." Bull. Amer. Math. Soc. 70 (1964): 727-729.

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