Remarks on weakly KKM maps in abstract convex spaces.
Représentation des algèbres universelles par des faisceaux
Representation of semigroups by products of topological spaces with prescribed cardinal functions
Representations into the hyperspace of a compact group.
Representations of commutative semigroups by products of metric -dimensional spaces
Representations of countable commutative semigroups by products of weakly homogeneous spaces
Results on common fixed points.
Results on fixed point theorems
Results On Non-Unique Fixed Points
Results on non-unique fixed points.
Results on the existence and convergence of best proximity points.
Rétractes Absolus de Voisinage Algébriques
2000 Mathematics Subject Classification: 54C55, 54H25, 55M20.We introduce the class of algebraic ANRs. It is defined by replacing continuous maps by chain mappings in Lefschetz’s characterization of ANRs. To a large extent, the theory of algebraic ANRs parallels the classical theory of ANRs. Every ANR is an algebraic ANR, but the class of algebraic ANRs is much larger; the most striking difference between these classes is that every locally equiconnected metrisable space is an algebraic ANR, whereas...
Retral spaces and continua with the fixed point property
We show that every retral continuum with the fixed point property is locally connected. It follows that an indecomposable continuum with the fixed point property is not a retract of a topological group.
Revisiting Cauty's proof of the Schauder conjecture.
RIC-расширения и структура расширений минимальных полугрупп преобразований
Rings of maps: sequential convergence and completion
The ring of all real-valued measurable functions, carrying the pointwise convergence, is a sequential ring completion of the subring of all continuous functions and, similarly, the ring of all Borel measurable subsets of is a sequential ring completion of the subring of all finite unions of half-open intervals; the two completions are not categorical. We study -rings of maps and develop a completion theory covering the two examples. In particular, the -fields of sets form an epireflective...
Roots of continuous piecewise monotone maps of an interval.
Rotation sets for graph maps of degree 1
For a continuous map on a topological graph containing a loop it is possible to define the degree (with respect to the loop ) and, for a map of degree , rotation numbers. We study the rotation set of these maps and the periods of periodic points having a given rotation number. We show that, if the graph has a single loop then the set of rotation numbers of points in has some properties similar to the rotation set of a circle map; in particular it is a compact interval and for every rational...
Rotation sets for some non-continuous maps of degree one.
Rotation sets for subshifts of finite type
For a dynamical system (X,f) and a function the rotation set is defined. The case when (X,f) is a transitive subshift of finite type and φ depends on the cylinders of length 2 is studied. Then the rotation set is a convex polyhedron. The rotation vectors of periodic points are dense in the rotation set. Every interior point of the rotation set is a rotation vector of an ergodic measure.