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
Recurrent points and discrete points for elementary amenable groups.
Relatively realcompact sets and nearly pseudocompact spaces
A space is said to be nearly pseudocompact iff is dense in . In this paper relatively realcompact sets are defined, and it is shown that a space is nearly pseudocompact iff every relatively realcompact open set is relatively compact. Other equivalences of nearly pseudocompactness are obtained and compared to some results of Blair and van Douwen.
Remarks on Cartesian products
Rings Of Real-Valued Functions And The Finite Subcovering Property.
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.