Locally eventually contractive Fixed-Point Mappings.
Locally minimal topological groups and their embeddings into products of -bounded groups
It is proven that an infinite-dimensional Banach space (considered as an Abelian topological group) is not topologically isomorphic to a subgroup of a product of -compact (or more generally, -bounded) topological groups. This answers a question of M. Tkachenko.
Locally Sierpinski Quotients.
Longer chains of idempotents in βG
Given idempotents e and f in a semigroup, e ≤ f if and only if e = fe = ef. We show that if G is a countable discrete group, p is a right cancelable element of G* = βG∖G, and λ is a countable ordinal, then there is a strictly decreasing chain of idempotents in , the smallest compact subsemigroup of G* with p as a member. We also show that if S is any infinite subsemigroup of a countable group, then any nonminimal idempotent in S* is the largest element of such a strictly decreasing chain of idempotents....
Losing Hausdorff dimension while generating pseudogroups
Considering different finite sets of maps generating a pseudogroup G of locally Lipschitz homeomorphisms between open subsets of a compact metric space X we arrive at a notion of a Hausdorff dimension of G. Since , the dimension loss can be considered as a “topological price” one has to pay to generate G. We collect some properties of and (for example, both of them are invariant under Lipschitz isomorphisms of pseudogroups) and we either estimate or calculate for pseudogroups arising...
Luzin sets are additive
Lyapunov quasi-stable trajectories
We introduce the notions of Lyapunov quasi-stability and Zhukovskiĭ quasi-stability of a trajectory in an impulsive semidynamical system defined in a metric space, which are counterparts of corresponding stabilities in the theory of dynamical systems. We initiate the study of fundamental properties of those quasi-stable trajectories, in particular, the structures of their positive limit sets. In fact, we prove that if a trajectory is asymptotically Lyapunov quasi-stable, then its limit set consists...
Lyapunov's direct method in abstract local semi-flows
Mann iterates of directionally nonexpansive mappings in hyperbolic spaces.
Mann iteration converges faster than Ishikawa iteration for the class of Zamfirescu operators.
Mapping theorems for compacta with an arbitrary involution
Maps of the interval Ljapunov stable on the set of nonwandering points.
Marczewski sets in the Hashimoto topologies for measure and category
Marczewski sets, measure and the Baire property
Markov partitions and
Matsumoto -groups associated to certain shift spaces.
Maximal distributional chaos of weighted shift operators on Köthe sequence spaces
During the last ten some years, many research works were devoted to the chaotic behavior of the weighted shift operator on the Köthe sequence space. In this note, a sufficient condition ensuring that the weighted shift operator defined on the Köthe sequence space exhibits distributional -chaos for any and any is obtained. Under this assumption, the principal measure of is equal to 1. In particular, every Devaney chaotic shift operator exhibits distributional -chaos for any .
Maximal equicontinuous factors and cohomology for tiling spaces
We study the homomorphism induced on cohomology by the maximal equicontinuous factor map of a tiling space. We will see that in degree one this map is injective and has torsion free cokernel. We show by example, however, that, in degree one, the cohomology of the maximal equicontinuous factor may not be a direct summand of the tiling cohomology.
Maximal inverse subsemigroups of S(Sn).
Maximal scrambled sets for simple chaotic functions.
This paper is a continuation of [1], where a explicit description of the scrambled sets of weakly unimodal functions of type 2∞ was given. Its aim is to show that, for an appropriate non-trivial subset of the above family of functions, this description can be made in a much more effective and informative way.