Expanding attractors
Expanding Maps of Solenoids.
Expansive Automorphisms in Compact Groups.
Expansive transformation semigroups of endomorphisms
Expansiveness on Compact Piecewise Linear Manifolds.
Extended contraction principle.
Extension and reconstruction theorems for the Urysohn universal metric space
We prove some extension theorems involving uniformly continuous maps of the universal Urysohn space. As an application, we prove reconstruction theorems for certain groups of autohomeomorphisms of this space and of its open subsets.
Extension of point-finite partitions of unity
A subspace A of a topological space X is said to be -embedded ((point-finite)-embedded) in X if every (point-finite) partition of unity α on A with |α| ≤ γ extends to a (point-finite) partition of unity on X. The main results are: (Theorem A) A subspace A of X is (point-finite)-embedded in X iff it is -embedded and every countable intersection B of cozero-sets in X with B ∩ A = ∅ can be separated from A by a cozero-set in X. (Theorem B) The product A × [0,1] is (point-finite)-embedded in X...
Extension of the Kirk-Saliga fixed point theorem.
Extension operators on balls and on spaces of finite sets
We study extension operators between spaces of continuous functions on the spaces of subsets of X of cardinality at most n. As an application, we show that if is the unit ball of a nonseparable Hilbert space H equipped with the weak topology, then, for any 0 < λ < μ, there is no extension operator .
Extensions of best approximation and coincidence theorems.
Extensions of Borel Measurable Maps and Ranges of Borel Bimeasurable Maps
We prove an abstract version of the Kuratowski extension theorem for Borel measurable maps of a given class. It enables us to deduce and improve its nonseparable version due to Hansell. We also study the ranges of not necessarily injective Borel bimeasurable maps f and show that some control on the relative classes of preimages and images of Borel sets under f enables one to get a bound on the absolute class of the range of f. This seems to be of some interest even within separable spaces.
Extensions of Ćirić generalised contractions
Extensions of Ćirić's quasi-constraction in Banach spaces
Extensions of fixed point theorems of Ćirić
Extensions of generic measure-preserving actions
We show that, whenever is a countable abelian group and is a finitely-generated subgroup of , a generic measure-preserving action of on a standard atomless probability space extends to a free measure-preserving action of on . This extends a result of Ageev, corresponding to the case when is infinite cyclic.
Extensions of some Fixed Point Theorems of Rhoades, Ćirić, Maiti and Pal
Extensions of topological and semitopological groups and the product operation
The main results concern commutativity of Hewitt-Nachbin realcompactification or Dieudonné completion with products of topological groups. It is shown that for every topological group that is not Dieudonné complete one can find a Dieudonné complete group such that the Dieudonné completion of is not a topological group containing as a subgroup. Using Korovin’s construction of -dense orbits, we present some examples showing that some results on topological groups are not valid for semitopological...
Extremal disconnectedness modulo dual filtrations.
Extreme points and descriptive sets
A class of closed, bounded, convex sets in the Banach space is shown to be a complete PCA set.