Topological AE(0)-groups

Alex Chigogidze

Displaying similar documents to “Topological AE(0)-groups”

Covering locally compact groups by less than $2^{ω}$ many translates of a compact nullset

Márton Elekes, Árpád Tóth (2007)

Fundamenta Mathematicae

Similarity:

Gruenhage asked if it was possible to cover the real line by less than continuum many translates of a compact nullset. Under the Continuum Hypothesis the answer is obviously negative. Elekes and Stepr mans gave an affirmative answer by showing that if $C_{E K}$ is the well known compact nullset considered first by Erdős and Kakutani then ℝ can be covered by cof() many translates of $C_{E K}$ . As this set has no analogue in more general groups, it was asked by Elekes and Stepr mans whether such a result...

Some remarks on Lorenzen $r$ -group of partly ordered groups

Jiří Močkoř, Angeliki Kontolatou (1996)

Czechoslovak Mathematical Journal

Similarity:

Regularity of sets with constant intrinsic normal in a class of Carnot groups

Marco Marchi (2014)

Annales de l’institut Fourier

Similarity:

In this Note, we define a class of stratified Lie groups of arbitrary step (that are called “groups of type $☆$ ” throughout the paper), and we prove that, in these groups, sets with constant intrinsic normal are vertical halfspaces. As a consequence, the reduced boundary of a set of finite intrinsic perimeter in a group of type $☆$ is rectifiable in the intrinsic sense (De Giorgi’s rectifiability theorem). This result extends the previous one proved by Franchi, Serapioni & Serra Cassano...

Plane and layer $(p 2, 2^{l})$ symmetry groups

S. V. Jablan (1990)

Matematički Vesnik

Similarity:

Compact Abelian groups and extensions of Haar measures

A. Hulanicki

Similarity:

ContentsIntroduction.................................................................................................................... 31. Preliminaries (topology measure).................................................................... 32. Problems and the theorem.................................................................................... 73. Preliminaries (abstract groups, Cartesian products)....................................... 94. Preliminaries (automorphisms, duality...

Plane and layer $(p^{p r i m e}, 2^{l})$ symmetry groups

S. V. Jablan (1990)

Matematički Vesnik

Similarity:

For Coxeter groups $z^{| g |}$ is a coefficient of a uniformly bounded representation

Tadeusz Januszkiewicz (2002)

Fundamenta Mathematicae

Similarity:

We prove the theorem in the title by constructing an action of a Coxeter group on a product of trees.

Arhangel'skiĭ sheaf amalgamations in topological groups

Boaz Tsaban, Lyubomyr Zdomskyy (2016)

Fundamenta Mathematicae

Similarity:

We consider amalgamation properties of convergent sequences in topological groups and topological vector spaces. The main result of this paper is that, for arbitrary topological groups, Nyikos’s property $α_{1.5}$ is equivalent to Arhangel’skiĭ’s formally stronger property α₁. This result solves a problem of Shakhmatov (2002), and its proof uses a new perturbation argument. We also prove that there is a topological space X such that the space $C_{p} (X)$ of continuous real-valued functions on X with the...

On groups of essential values of topological cylinder cocycles over minimal rotations

Mieczysław K. Mentzen (2003)

Colloquium Mathematicae

Similarity:

A theory of essential values of cocycles over minimal rotations with values in locally compact Abelian groups, especially $ℝ^{m}$ , is developed. Criteria for such a cocycle to be conservative are given. The group of essential values of a cocycle is described.

A problem of Kollár and Larsen on finite linear groups and crepant resolutions

Robert Guralnick, Pham Tiep (2012)

Journal of the European Mathematical Society

Similarity:

The notion of age of elements of complex linear groups was introduced by M. Reid and is of importance in algebraic geometry, in particular in the study of crepant resolutions and of quotients of Calabi–Yau varieties. In this paper, we solve a problem raised by J. Kollár and M. Larsen on the structure of finite irreducible linear groups generated by elements of age $\leq 1$ . More generally, we bound the dimension of finite irreducible linear groups generated by elements of bounded deviation....

Extremal phenomena in certain classes of totally bounded groups

W. W. Comfort, Lewis C. Robertson

Similarity:

For various pairs of topological properties such that P ⇒ Q, we consider two questions: (A) Does every topological group topology with P extend properly to a topological group topology with Q, and (B) must a topological group with P have a proper dense subgroup with Q? We obtain negative results and positive results. Principal among the latter is the statement that any pseudocompact group G of uncountable weight which satisfies any of the following three conditions has both a strictly...

Homomorphic images of $ℝ$ -factorizable groups

Mihail G. Tkachenko (2006)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

It is well known that every $ℝ$ -factorizable group is $ω$ -narrow, but not vice versa. One of the main problems regarding $ℝ$ -factorizable groups is whether this class of groups is closed under taking continuous homomorphic images or, alternatively, whether every $ω$ -narrow group is a continuous homomorphic image of an $ℝ$ -factorizable group. Here we show that the second hypothesis is definitely false. This result follows from the theorem stating that if a continuous homomorphic image of an $ℝ$ -factorizable...

On the foundations of k-group theory

W. F. Lamartin

Similarity:

CONTENTSIntroduction................... 51. k-spaces.................... 62. k-groups.................... 14References..................... 32