Ramsey theoretic consequences of some new results about algebra in the Stone-Čech compactification.
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 .
∗ This work was partially supported by the National Foundation for Scientific Researches at the Bulgarian Ministry of Education and Science under contract no. MM-427/94.In this paper the notion of SR-proximity is introduced and in virtue of it some new proximity-type descriptions of the ordered sets of all (up to equivalence) regular, resp. completely regular, resp. locally compact extensions of a topological space are obtained. New proofs of the Smirnov Compactification Theorem [31] and of the...
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.