Construction de revêtements du groupe conforme d’un espace vectoriel muni d’une «métrique» de type
Various techniques are presented for constructing (p) sets which are not for all . The main result is that there is a (4) set in the dual of any compact abelian group which is not for all . Along the way to proving this, new constructions are given in dual groups in which constructions were already known of (p) not sets, for certain values of . The main new constructions in specific dual groups are:– there is a (2k) set which is not in for all , and , and in ( a prime,...
The action of the conformal group on may be characterized in differential geometric terms, even locally: a theorem of Liouville states that a map between domains and in whose differential is a (variable) multiple of a (variable) isometry at each point of is the restriction to of a transformation , for some in . In this paper, we consider the problem of characterizing the action of a more general semisimple Lie group on the space , where is a parabolic subgroup. We solve...
We provide a generalization of continued fractions to the Heisenberg group. We prove an explicit estimate on the rate of convergence of the infinite continued fraction and several surprising analogs of classical formulas about continued fractions.
In this paper, we show that it is possible to extend the Ellis theorem, establishing the relations between axioms of a topological group on a new class of spaces containing all countably compact spaces in the case of Abelian group structure. We extend statements of the Ellis theorem concerning separate and joint continuity of group inverse on the class of spaces that gives some new examples and statements for the -theory and theory of topologically homogeneous spaces.