There are uncountably many topological types of locally finite trees
نویسندگان
چکیده
منابع مشابه
There are uncountably many topological types of locally finite trees
Consider two locally finite rooted trees as equivalent if each of them is a topological minor of the other, with an embedding preserving the tree-order. Answering a question of van der Holst, we prove that there are uncountably many equivalence classes.
متن کاملHow Many Types Are There?
We consider an revealed preference based method which will partition consumer microdata into an approximate minimal number of preference types such that the data are perfectly rationalisable by standard utility theory. This provides a simple, nonparametric and theory-driven way of investigating unobserved preference heterogeneity in empirical data, and easily extends to any choice model which h...
متن کاملOn Groups with Uncountably Many Subgroups of Finite Index
Let K be the kernel of an epimorphism χ : G → Z, for G a finitely presented group. If K has uncountably many normal subgroups of finite index r, then K has uncountably many subgroups (not necessarily normal) of any finite index greater than r. In particular, this is the case whenever G is subgroup separable and K is nonfinitely generated. Assume that G has an abelian HNN base contained in K. If...
متن کاملSpaces of Uncountably Many Dimensions*
Riemann in his Habilitations Schrift of 1854 suggested the notion of ^-dimensional space (where n is a natural number) as an extension of the notion of three-dimensional euclidean space. Hubert extended the notion still further by defining a space of a countably infinite number of dimensions. Fréchetf in 1908 defined two other spaces of countably many dimensions, which he called D„ and J3W. Tyc...
متن کاملDistinguishability of Locally Finite Trees
The distinguishing number ∆(X) of a graph X is the least positive integer n for which there exists a function f : V (X) → {0, 1, 2, · · · , n−1} such that no nonidentity element of Aut(X) fixes (setwise) every inverse image f−1(k), k ∈ {0, 1, 2, · · · , n − 1}. All infinite, locally finite trees without pendant vertices are shown to be 2distinguishable. A proof is indicated that extends 2-disti...
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: Journal of Combinatorial Theory, Series B
سال: 2006
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2006.02.001