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.
Rough and strongly rough norms on Banach spaces
Rozklad elementární křivky na Jordanovy křivky
Rozklad přímky na shodné trojbodové množiny
r-Realcompact spaces
A new generalization of realcompactness based on ultrafilters of regular -subsets is introduced. Its relationship with realcompactness, almost realcompactness, almost* realcompactness, c-realcompactness is examined. Some of the properties of the newly introduced space is studied as well.
Rudin's Dowker space in the extension with a Suslin tree
We introduce a generalization of a Dowker space constructed from a Suslin tree by Mary Ellen Rudin, and the rectangle refining property for forcing notions, which modifies the one for partitions due to Paul B. Larson and Stevo Todorčević and is stronger than the countable chain condition. It is proved that Martin's Axiom for forcing notions with the rectangle refining property implies that every generalized Rudin space constructed from Aronszajn trees is non-Dowker, and that the same can be forced...