Geodesic
Regularity of Richardson's Compactification
Canadian journal of mathematics, Tome 26 (1974) no. 6, pp. 1289-1293

Voir la notice de l'article provenant de la source Cambridge University Press

In [7] Richardson constructed a Stone-Čech type compactification R(E) of a Hausdorff convergence space E. Two questions arise in this regard. First, when is R(E) homeomorphic to β(E), β(E) the topological Stone-Čech compactification of E, for a Tychonoff topological space E? Second, if E is a regular convergence space, when is R(E) regular? The last question is motivated by the study of regular compactifications in [6]. In section 2 it will be shown that a necessary and sufficient condition in answer to both questions, is that α = cl(α) for each nonconvergent ultrafilter α on E. 
Gazik, R. J. Regularity of Richardson's Compactification. Canadian journal of mathematics, Tome 26 (1974) no. 6, pp. 1289-1293. doi: 10.4153/CJM-1974-123-7
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