Real closed rings, I. Residue rings of rings of continuous functions
Real complete and K-complete proximity
Real ideals in the maximal ring of quotients of
Real maximal round filters in proximity spaces
Realcompactification and repleteness of Wallman spaces.
Realcompactification of frames
We give a construction of Wallman-type realcompactifications of a frame by considering regular sub -frames the join of which generates . In particular, we show that the largest such regular sub -frame gives rise to the universal realcompactification of .
Realcompactness and spaces of vector-valued functions
It is shown that the existence of a biseparating map between a large class of spaces of vector-valued continuous functions A(X,E) and A(Y,F) implies that some compactifications of X and Y are homeomorphic. In some cases, conditions are given to warrant the existence of a homeomorphism between the realcompactifications of X and Y; in particular we find remarkable differences with respect to the scalar context: namely, if E and F are infinite-dimensional and T: C*(X,E) → C*(Y,F) is a biseparating...
Realcompactness and Wallman realcompactification
Realisierung und Auswahlaxiom
Realization of Cartesian Closed Topological Hulls.
Realization of mappings
Realizations of closure spaces by set systems
Realizations of topologies and closure operators by set systems and by neighbourhoods
Realizing homomorphisms of category algebras
Real-valued continuous functions and the span of continua
Real-valued functions on Alexandroff (zero-set) spaces
Real-valued functions on certain semi-metric spaces
Recent development of theory of uniform spaces
Recent developments in the theory of Borel reducibility
Let E₀ be the Vitali equivalence relation and E₃ the product of countably many copies of E₀. Two new dichotomy theorems for Borel equivalence relations are proved. First, for any Borel equivalence relation E that is (Borel) reducible to E₃, either E is reducible to E₀ or else E₃ is reducible to E. Second, if E is a Borel equivalence relation induced by a Borel action of a closed subgroup of the infinite symmetric group that admits an invariant metric, then either E is reducible to a countable...
Recent research in hyperspace theory.