and axioms in fuzzy topology
-continuous functions.
-compact spaces and -connected spaces.
Radical ideals and coherent frames
It follows from Stone Duality that Hochster's results on the relation between spectral spaces and prime spectra of rings translate into analogous, formally stronger results concerning coherent frames and frames of radical ideals of rings. Here, we show that the latter can actually be obtained without Stone Duality, proving them in Zermelo-Fraenkel set theory and thereby sharpening the original results of Hochster.
Radon spaces which are not -fragmentable
Ramsey theoretic consequences of some new results about algebra in the Stone-Čech compactification.
Rapid ultrafilter need not be Q-point
Rapport entre l'ensemble des ultrafiltres admettant un ultrafiltre donné pour image et l'ensemble des images de cet ultrafiltre
Rare -continuity.
Rational spaces and the property of universality
Real closed rings, I. Residue rings of rings of continuous functions
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
Rectangular covers of products missing diagonals
We give a characterization of a paracompact -space to have a -diagonal in terms of three rectangular covers of . Moreover, we show that a local property and a global property of a space are given by the orthocompactness of .
Recurrent and weakly recurrent points in G.
Recurrent functions and semigroups.
Recurrent functions on compact spaces.
Recurrent points and discrete points for elementary amenable groups.