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Property Q.

Bandy, C. (1991)

International Journal of Mathematics and Mathematical Sciences

Propriétés topologiques et combinatoires des échelles de numération

Guy Barat, Tomasz Downarowicz, Anzelm Iwanik, Pierre Liardet (2000)

Colloquium Mathematicae

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.

Proto-metrizable fuzzy topological spaces

Francisco Gallego Lupiañez (1999)

Kybernetika

In this paper we define for fuzzy topological spaces a notion corresponding to proto-metrizable topological spaces. We obtain some properties of these fuzzy topological spaces, particularly we give relations with non-archimedean, and metrizable fuzzy topological spaces.

Proximal set-open topologies

Anna Di Concilio, Som Naimpally (2000)

Bollettino dell'Unione Matematica Italiana

Introduciamo una nuova classe di topologie in spazi di funzioni derivanti da prossimità sul rango, che denotiamo sinteticamente PSOTs, acronimo di proximal set-open topologies. Le PSOTs sono una naturale generalizzazione delle classiche topologie di tipo set-open quando l'ordinaria inclusione viene sostituita con l'inclusione stretta associata ad una prossimità. Molte e note topologie di tipo set-open connesse a speciali networks sono esempi di PSOTs. Ogni PSOT è contraibile ad un sottospazio chiuso...

Proximality in Pisot tiling spaces

Marcy Barge, Beverly Diamond (2007)

Fundamenta Mathematicae

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 φ has pure discrete spectrum, we describe the collection φ P of pairs of proximal tilings in φ in a natural way as a substitution tiling space. We show that if ψ is another such substitution, then φ and ψ are homeomorphic if and...

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