Every graph is a self-similar set.
Arenas, Francisco G., Sánchez-Granero, M.A. (2000)
Divulgaciones Matemáticas
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Displaying similar documents to “Extension of Lipschitz functions defined on metric subspaces of homogeneous type.”
Every graph is a self-similar set.
An invariant of bi-Lipschitz maps
Hossein Movahedi-Lankarani (1993)
Fundamenta Mathematicae
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A new numerical invariant for the category of compact metric spaces and Lipschitz maps is introduced. This invariant takes a value less than or equal to 1 for compact metric spaces that are Lipschitz isomorphic to ultrametric ones. Furthermore, a theorem is provided which makes it possible to compute this invariant for a large class of spaces. In particular, by utilizing this invariant, it is shown that neither a fat Cantor set nor the set is Lipschitz isomorphic to an ultrametric...
Fixed point theorems on S-metric spaces
Shaban Sedghi, Nguyen Van Dung (2014)
Matematički Vesnik
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On Kannan fixed point principle in generalized metric spaces.
Miheţ, Dorel (2009)
The Journal of Nonlinear Sciences and its Applications
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Poincaré Inequalities for Mutually Singular Measures
Andrea Schioppa (2015)
Analysis and Geometry in Metric Spaces
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Using an inverse system of metric graphs as in [3], we provide a simple example of a metric space X that admits Poincaré inequalities for a continuum of mutually singular measures.
A generalization of fixed point theorems in -metric spaces
Shaban Sedghi, Nabi Shobe, Abdelkrim Aliouche (2012)
Matematički Vesnik
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A general existence principle for fixed point theorems in -metric spaces.
Dhage, B.C., Pathan, A.M., Rhoades, B.E. (2000)
International Journal of Mathematics and Mathematical Sciences
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The universal separable metric space of Urysohn and isometric embeddings thereof in Вanach spaces
M. Holmes (1992)
Fundamenta Mathematicae
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This paper is an investigation of the universal separable metric space up to isometry U discovered by Urysohn. A concrete construction of U as a metric subspace of the space C[0,1] of functions from [0,1] to the reals with the supremum metric is given. An answer is given to a question of Sierpiński on isometric embeddings of U in C[0,1]. It is shown that the closed linear span of an isometric copy of U in a Banach space which contains the zero of the Banach space is determined up to...
Metric locally constant function on some subset of ultrametric space.
Gajić, Ljiljana (2005)
Novi Sad Journal of Mathematics
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Inverse Function Theorems and Jacobians over Metric Spaces
Luca Granieri (2014)
Analysis and Geometry in Metric Spaces
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We present inversion results for Lipschitz maps f : Ω ⊂ ℝN → (Y, d) and stability of inversion for uniformly convergent sequences. These results are based on the Area Formula and on the l.s.c. of metric Jacobians.
On robustness of the regularity property of maps
Alexander Ioffe (2003)
Control and Cybernetics
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On the gluing of hyperconvex metrics and diversities
Bożena Piątek (2014)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
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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.