Madalina Roxana Buneci
@utgjiu.ro
University Constantin Brancusi from Targu-Jiu
Scopus Publications
Scholar Citations
Scholar h-index
Scholar i10-index
Scopus Publications
Mădălina Buneci
American Mathematical Society (AMS)
Dana P. Williams raised in [Proc. Amer. Math. Soc., Ser. B 3 (2016), pp. 1–8] the following question: Must a second countable, locally compact, transitive groupoid have open range map? This paper gives a negative answer to that question. Although a second countable, locally compact transitive groupoid G G may fail to have open range map, we prove that we can replace its topology with a topology which is also second countable, locally compact, and with respect to which G G is a topological groupoid whose range map is open. Moreover, the two topologies generate the same Borel structure and coincide on the fibres of G G .
Viorica Mariela Ungureanu and Mădălina Roxana Buneci
Springer International Publishing
Mădălina Roxana Buneci and
American Institute of Mathematical Sciences (AIMS)
The purpose of this paper is to introduce a category whose objects are
discrete dynamical systems $( X,P,H,\\theta ) $ in the sense of
[6] and whose arrows will be defined starting from the notion of
groupoid morphism given in [10]. We shall also construct a
contravariant functor $( X,P,H,\\theta ) \\rightarrow $C* $( X,P,H,\\theta ) $ from the subcategory of discrete dynamical
systems for which $PP^{-1}$ is amenable to the category of C* -algebras, where C* $( X,P,H,\\theta ) $ is the C* -algebra associated to the groupoid $G( X,P,H,\\theta)$.
M. Buneci
Akademiai Kiado Zrt.
Kirill Mackenzie raised in [3] (p. 31) the following question: given a morphism F : Ω → Ω′, where Ω and Ω′ are topological groupoids and F is continuous on a neighborhood of the base in Ω, is it true that is Ω continuous everywhere?This paper gives a negative answer to that question. Moreover, we shall prove that for a locally compact groupoid Ω with non-singleton orbits and having open target projection, if we assume that the continuity of every morphism F on a neighborhood of the base in Ω implies the continuity of F everywhere, then the groupoid Ω must be locally transitive.