A p–compact group (see Dwyer–Wilkerson [8]) is a loop space X such that X is Fp –finite and that its classifying space BX is Fp –complete (see Andersen–Grodal– Møller–Viruel [2] and Dwyer–Wilkerson [11]). We recall that the p–completion of a compact Lie group G is a p–compact group if π0(G) is a p–group. Next, if C(ρ) denotes the centralizer of a group homomorphism ρ from a p–toral group to a c...

The existence of admissible vectors for a locally compact group is closely related to the group's profile. In the compact groups, according to Peter-weyl theorem, every irreducible representation has admissible vector. In this paper, the conditions under which the inverse of this case is being investigated has been investigated. Conditions such as views that are admissible and stable will get c...

We prove that the topological statement: “Any compact covering mapping between two Borel sets is inductively perfect” is equivalent to the set-theoretical statement: “ ∀α ∈ ωω , א 1 < א1”. The starting point of this work is the following topological problem: Problem. Is any compact covering mapping between two Borel spaces inductively perfect? We recall that if f : X → Y is a continuous and ont...

A locally compact T2-space is called a Franklin-Rajagopalan space (or FR-space) provided it has a countable discrete dense subset whose complement is homeomorphic to an ordinal with the order topology. We show that (1) every sequentially compact FR-space X can be identified with a space constructed from a tower T on w (X = X(T)), and (2) for an ultrafilter u on w, a sequentially compact FR-spac...

We propose to study the L-norm distance between classical and quantum phase space distributions, where for the latter we choose the Wigner function, as a global phase space indicator of quantum-classical correspondence. For example, this quantity should provide a key to understand the correspondence between quantum and classical Loschmidt echoes. We concentrate on fully chaotic systems with com...

Given a collection of documents and a query pattern, document retrieval is the problem of obtaining documents that are relevant to the query. The collection is available beforehand so that a data structure, called an index, can be built on it to speed up queries. While initially restricted to natural language text collections, document retrieval problems arise nowadays in applications like bioi...

MSC: 54G05 54F45 54D35