On locally connected connectifications (Q1304868)

A connectification of a space \(X\) is a connected topological space \(Y\) containing a dense (homeomorphic) copy of \(X\). The results of the article under review extend theorems of S. Watson and the reviewer [Houston J. Math. 19, No.~3, 469-481 (1993; Zbl 0837.54012))] by showing that each Hausdorff space with a countable \(\pi\)-base and in which regular closed sets are not \(H\)-closed has a locally connected connectification with countable remainder. As an immediate corollary, the Sorgenfrey line has such a connectification, thus answering a question posed by O. T. Alas, M. G. Tkachenko, V. V. Tkachuk and the reviewer (to appear in Commentationes Mathematicae Universitatis Carolinae). Another result implies that each dense-in-itself countable Hausdorff space has a locally connected \(T_2\) connectification.