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Open maps between Knaster continua

Carl Eberhart, J. Fugate, Shannon Schumann (1999)

Fundamenta Mathematicae

We investigate the set of open maps from one Knaster continuum to another. A structure theorem for the semigroup of open induced maps on a Knaster continuum is obtained. Homeomorphisms which are not induced are constructed, and it is shown that the induced open maps are dense in the space of open maps between two Knaster continua. Results about the structure of the semigroup of open maps on a Knaster continuum are obtained and two questions about the structure are posed.

Openly factorizable spaces and compact extensions of topological semigroups

Taras O. Banakh, Svetlana Dimitrova (2010)

Commentationes Mathematicae Universitatis Carolinae

We prove that the semigroup operation of a topological semigroup S extends to a continuous semigroup operation on its Stone-Čech compactification β S provided S is a pseudocompact openly factorizable space, which means that each map f : S → Y to a second countable space Y can be written as the composition f = g ∘ p of an open map p : X → Z onto a second countable space Z and a map g : Z → Y . We present a spectral characterization of openly factorizable spaces and establish some properties of such spaces.

Orbit coupling

Hans-Otto Georgii (1997)

Annales de l'I.H.P. Probabilités et statistiques

Orbit equivalence and Kakutani equivalence with Sturmian subshifts

P. Dartnell, F. Durand, A. Maass (2000)

Studia Mathematica

Using dimension group tools and Bratteli-Vershik representations of minimal Cantor systems we prove that a minimal Cantor system and a Sturmian subshift are topologically conjugate if and only if they are orbit equivalent and Kakutani equivalent.

Ordered K-theoryand minimal symbolic dynamical systems

Christian Skau (2000)

Colloquium Mathematicae

Recently a new invariant of K-theoretic nature has emerged which is potentially very useful for the study of symbolic systems. We give an outline of the theory behind this invariant. Then we demonstrate the relevance and power of the invariant, focusing on the families of substitution minimal systems and Toeplitz flows.

Ordinals in topological groups

Raushan Z. Buzyakova (2007)

Fundamenta Mathematicae

We show that if an uncountable regular cardinal τ and τ + 1 embed in a topological group G as closed subspaces then G is not normal. We also prove that an uncountable regular cardinal cannot be embedded in a torsion free Abelian group that is hereditarily normal. These results are corollaries to our main results about ordinals in topological groups. To state the main results, let τ be an uncountable regular cardinal and G a T₁ topological group. We prove, among others, the following statements:...

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