Retracts and homotopies for multi-maps
Retracts in equiconnected spaces.
Retracts of the Sorgenfrey line
Retracts of Tychonoff and normal spaces.
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.
R-fuzzy Strongly Preopen Sets in Fuzzy Topological Spaces
Richtungsräume und Richtungsdimension
RIC-расширения и структура расширений минимальных полугрупп преобразований
Right simple subsemigroups and right subgroups of compact convergence semigroups.
Rigid extensions of -groups of continuous functions
Let , and denote the -groups of integer-valued, rational-valued and real-valued continuous functions on a topological space , respectively. Characterizations are given for the extensions to be rigid, major, and dense.
Rigid P-spaces
Ring epimorphisms and .
Rings of continuous functions vanishing at infinity
We prove that a Hausdorff space is locally compact if and only if its topology coincides with the weak topology induced by . It is shown that for a Hausdorff space , there exists a locally compact Hausdorff space such that . It is also shown that for locally compact spaces and , if and only if . Prime ideals in are uniquely represented by a class of prime ideals in . -compact spaces are introduced and it turns out that a locally compact space is -compact if and only if every...
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...
Rings of Real-Valued Continuous Functions. II.
Rings Of Real-Valued Functions And The Finite Subcovering Property.
Roots of continuous piecewise monotone maps of an interval.
Rosenthal compacta and NIP formulas
We apply the work of Bourgain, Fremlin and Talagrand on compact subsets of the first Baire class to show new results about ϕ-types for ϕ NIP. In particular, we show that if M is a countable model, then an M-invariant ϕ-type is Borel-definable. Also, the space of M-invariant ϕ-types is a Rosenthal compactum, which implies a number of topological tameness properties.
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...