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Étude de la classification topologique des fonctions unimodales

Michel Cosnard (1985)

Annales de l'institut Fourier

À l’aide de la théorie des itinéraires et des suites de tricotage, nous étudions la conjugaison topologique des fonctions unimodales. Nous introduisons la notion de conjugaison macroscopique, caractérisée par l’égalité des suites de tricotage. Puis nous présentons un théorème de classification des fonctions unimodales. Pour illustrer ces résultats, nous montrons que l’ensemble des solutions de l’équation de Feigenbaum contient une infinité de classes topologiques.

Examples of sequential topological groups under the continuum hypothesis

Alexander Shibakov (1996)

Fundamenta Mathematicae

Using CH we construct examples of sequential topological groups: 1. a pair of countable Fréchet topological groups whose product is sequential but is not Fréchet, 2. a countable Fréchet and α 1 topological group which contains no copy of the rationals.

Extension of multisequences and countably uniradial classes of topologies

Szymon Dolecki, Andrzej Starosolski, Stephen W. Watson (2003)

Commentationes Mathematicae Universitatis Carolinae

It is proved that every non trivial continuous map between the sets of extremal elements of monotone sequential cascades can be continuously extended to some subcascades. This implies a result of Franklin and Rajagopalan that an Arens space cannot be continuously non trivially mapped to an Arens space of higher rank. As an application, it is proved that if for a filter ℋ on ω , the class of ℋ -radial topologies contains each sequential topology, then it includes the class of subsequential topologies....

Extraresolvability and cardinal arithmetic

Ofelia Teresa Alas, Salvador García-Ferreira, Artur Hideyuki Tomita (1999)

Commentationes Mathematicae Universitatis Carolinae

Following Malykhin, we say that a space X is extraresolvable if X contains a family 𝒟 of dense subsets such that | 𝒟 | > Δ ( X ) and the intersection of every two elements of 𝒟 is nowhere dense, where Δ ( X ) = min { | U | : U is a nonempty open subset of X } is the dispersion character of X . We show that, for every cardinal κ , there is a compact extraresolvable space of size and dispersion character 2 κ . In connection with some cardinal inequalities, we prove the equivalence of the following statements: 1) 2 κ < 2 κ + , 2) ( κ + ) κ is extraresolvable and...

Extraresolvability of balleans

Igor V. Protasov (2007)

Commentationes Mathematicae Universitatis Carolinae

A ballean is a set endowed with some family of balls in such a way that a ballean can be considered as an asymptotic counterpart of a uniform topological space. We introduce and study a new cardinal invariant of a ballean, the extraresolvability, which is an asymptotic reflection of the corresponding invariant of a topological space.

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