Another characterization of hyperbolic diameter diminishing to zero IFSs
نویسندگان
چکیده
منابع مشابه
On the Diameter of Hyperbolic Random Graphs
Large real-world networks are typically scale-free. Recent research has shown that such graphs are described best in a geometric space. More precisely, the internet can be mapped to a hyperbolic space such that geometric greedy routing performs close to optimal (Boguná, Papadopoulos, and Krioukov. Nature Communications, 1:62, 2010). This observation pushed the interest in hyperbolic networks as...
متن کاملCounting Hyperbolic Manifolds with Bounded Diameter
Let ρn(V ) be the number of complete hyperbolic manifolds of dimension n with volume less than V . Burger, Gelander, Lubotzky, and Moses[2] showed that when n ≥ 4 there exist a, b > 0 depending on the dimension such that aV logV ≤ log ρn(V ) ≤ bV logV, for V ≫ 0. In this note, we use their methods to bound the number of hyperbolic manifolds with diameter less than d and show that the number gro...
متن کاملOf Another Characterization Of
Stepr¯ ans provided a characterization of βN \ N in the ℵ 2-Cohen model that is much in the spirit of Parovičenko's characterization of this space under CH. A variety of the topological results established in the Cohen model can be deduced directly from the properties of βN \ N or P(N)/fin that feature in Stepr¯ ans' result.
متن کاملGalois-theoretic Characterization of Isomorphism Classes of Monodromically Full Hyperbolic Curves of Genus Zero
Let l be a prime number. In the present paper, we prove that the isomorphism class of an l-monodromically full hyperbolic curve of genus zero over a finitely generated extension of the field of rational numbers is completely determined by the kernel of the natural pro-l outer Galois representation associated to the hyperbolic curve. This result can be regarded as a genus zero analogue of a resu...
متن کاملAnother Characterization of Trees
It is proved that a continuum is a tree if and only if each two connected subsets meet in a connected set. In this note a continuum is a compact connected Hausdorff space. A tree is a continuum in which distinct points are never conjugate [6], i.e., any two distinct points are separated by the deletion of some third point. A dendrite is a metrizable tree. The literature is replete with characte...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Carpathian Journal of Mathematics
سال: 2021
ISSN: 1843-4401,1584-2851
DOI: 10.37193/cjm.2021.02.08