A construction for topological extensions (Q2891029)

The results are an extension of [\textit{C. Ganesa Moorthy} and \textit{K. T. Rajambal}, in: K. S. Lakshmi (ed.) et al., Proceedings of the international conference on analysis and its applications, Chennai, India, December 6--9, 2000. New Delhi: Allied Publishers Ltd. 67--71 (2001; Zbl 0987.54028)]. An extension obtained and used to give all Hausdorff compactifications in [loc. cit.] becomes regular, if its members which are a type of o-filter bases, satisfy a condition. It is proved that every regular Hausdorff extension of a regular space can be obtained in this way. A necessary and sufficient condition is obtained for two regular Hausdorff extensions to be comparable. Every collection of Hausdorff compactifications is shown to have a supremum. Some results are extended to convex compactifications of a topological vector space.