A characterization of realcompactness in terms of the topology of pointwise convergence on the function space
A characterization of the -realcompact space
A general realcompactification method
A generalization of -compact spaces
A note on realcompact unions
A note on Rudin's example of Dowker space
About remainders in compactifications of homogeneous spaces
We prove a dichotomy theorem for remainders in compactifications of homogeneous spaces: given a homogeneous space , every remainder of is either realcompact and meager or Baire. In addition we show that two other recent dichotomy theorems for remainders of topological groups due to Arhangel’skii cannot be extended to homogeneous spaces.
Almost realcompactness
We provide a new generalization of realcompactness based on ultrafilters of cozero sets and contrast it with almost realcompactness.
Applications of complete families of continuous functions to the theory of -spaces
Approximation of with countable subsets of and calibers of the space
A-realcompact spaces.
Relations between homomorphisms on a real function algebra and different properties (such as being inverse-closed and closed under bounded inversion) are studied.