Linear right ideal nearrings.
Linking contractive self-mappings and cyclic Meir-Keeler contractions with Kannan self-mappings.
Local constribution to the Lefschetz fixes point formula.
Local convexity in topological lattices
Local expansions and accretive mappings.
Local expansions, derivatives, and fixed points
Local return rates in Sturmian subshifts
Local return rates in substitutive subshifts
Locally compact Baer rings.
Locally compact F-spaces, sub-stonean spaces and quotients of locally compact groups.
Locally compact topologically nil and monocompact PI-rings.
Locally connected exceptional minimal sets of surface homeomorphisms
We deal with locally connected exceptional minimal sets of surface homeomorphisms. If the surface is different from the torus, such a minimal set is either finite or a finite disjoint union of simple closed curves. On the torus, such a set can admit also a structure similar to that of the Sierpiński curve.
Locally equicontinuous dynamical systems
A new class of dynamical systems is defined, the class of “locally equicontinuous systems” (LE). We show that the property LE is inherited by factors as well as subsystems, and is closed under the operations of pointed products and inverse limits. In other words, the locally equicontinuous functions in form a uniformly closed translation invariant subalgebra. We show that WAP ⊂ LE ⊂ AE, where WAP is the class of weakly almost periodic systems and AE the class of almost equicontinuous systems....
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...