Products of topological spaces represent any semigroup (Preliminary communication)
Prolongational centers and their depths
In 1926 Birkhoff defined the center depth, one of the fundamental invariants that characterize the topological structure of a dynamical system. In this paper, we introduce the concepts of prolongational centers and their depths, which lead to a complete family of topological invariants. Some basic properties of the prolongational centers and their depths are established. Also, we construct a dynamical system in which the depth of a prolongational center is a prescribed countable ordinal.
Prolongationally stable discrete flows
Proper actions of locally compact groups on equivariant absolute extensors
Let G be a locally compact Hausdorff group. We study equivariant absolute (neighborhood) extensors (G-AE's and G-ANE's) in the category G-ℳ of all proper G-spaces that are metrizable by a G-invariant metric. We first solve the linearization problem for proper group actions by proving that each X ∈ G-ℳ admits an equivariant embedding in a Banach G-space L such that L∖{0} is a proper G-space and L∖{0} ∈ G-AE. This implies that in G-ℳ the notions of G-A(N)E and G-A(N)R coincide. Our embedding result...
Properties of a pair of functions which generate a dense subsemigroup of S(X).
Properties of fixed point set of a multivalued map.
Properties of monotone mappings in partially ordered sets.
Property P in G-metric spaces.
Propiedades topológicas de los grupos de isometría de un grupo reticulado.
This paper deals with the topological properties of groups of isometries of lattice-ordered groups and f-rings. The topologies considered are order-topology and the topology defined by null-sequences.
Propriétés topologiques et combinatoires des échelles de numération
Topological and combinatorial properties of dynamical systems called odometers and arising from number systems are investigated. First, a topological classification is obtained. Then a rooted tree describing the carries in the addition of 1 is introduced and extensively studied. It yields a description of points of discontinuity and a notion of low scale, which is helpful in producing examples of what the dynamics of an odometer can look like. Density of the orbits is also discussed.
Proximality in Pisot tiling spaces
A substitution φ is strong Pisot if its abelianization matrix is nonsingular and all eigenvalues except the Perron-Frobenius eigenvalue have modulus less than one. For strong Pisot φ that satisfies a no cycle condition and for which the translation flow on the tiling space has pure discrete spectrum, we describe the collection of pairs of proximal tilings in in a natural way as a substitution tiling space. We show that if ψ is another such substitution, then and are homeomorphic if and...
Pseudocompact refinements of compact group topologies.
Pseudocompactness - from compactifications to multiplication of borel sets
Pure measures
Purely infinite -algebras arising from dynamical systems
Purely infinite C*-algebras from boundary actions of discrete groups.