Contribution à la topologie des ensembles dénombrables

Operators on C[0,1] preserving copies of asymptotic ℓ1 spaces

“…Then F M would be pointwise compact for some M ∈ [N], M = (m i ). It follows by the Mazurkiewicz-Sierpinski theorem [29], that F M is homeomorphic to the ordinal interval [1, ω β d], for some β < ω 1 and d ∈ N. Set α = β + 1. It is easily seen that F M is hereditary and so we can apply the result of [19] (see also [23]) to obtain an infinite subset L of {m 2i : i ∈ N} so that …”

Homeomorphisms on compact metric spaces with finite derived length

“…Now, suppose X is not compact. Since X is separable, it is known that X is homeomorphic to a subspace of ω n for some n (See [8]). So, it is enough to consider the number of G S −orbits in X, where S ⊂ X ⊂ ω n .…”

Limits of dihedral groups

“…In Sect. 5 we describe the set of limits of dihedral groups on m generators: We use a theorem of Mazurkiewicz and Sierpinski [13] on Cantor-Bendixson invariants of countable compact spaces to prove the last result. For comparison, the set of abelian marked groups on m generators is homeomorphic to ω m + 1.…”