The abstract of the talk (see below) may be downloaded in one of the following formats:
A space X is called ( pathwise ) connectifiable if it can be embedded as a dense subspace of a ( pathwise ) connected Hausdorff space Y; if such is the case, Y is called a ( pathwise ) connectification of X. In this lecture we provide a survey of the most important results obtained by several authors. Moreover, we will give a rather complete endup-to-date list of the major open problems in this field. \begin{thebibliography}{10} \bibitem{ATTW96} O.\,T.~Alas, M.\,G.~Tka\v cenko, V.\,V.~Tkachuk, R.\,G.~Wilson, {\em Connectifying some spaces}, Topology Appl., {\bf 71} (1996), no.~3, 203--215. 54D05 (54A35) \bibitem{ATTW99} O.\,T.~Alas, M.\,G.~Tka\v cenko, V.\,V.~Tkachuk, R.\,G.~Wilson, {\em Connectedness and local connectedness of topological groups and extensions}, Comment. Math. Univ. Carolin. {\bf40} (1999), no.~4, 735--753. \bibitem{CFL2001} C.~Costantini, A.~Fedeli, A.~Le Donne, {\em Filters and pathwise connectifications }, Rend. Istit. Mat. Univ. Trieste , XXXII (2001), 1--15. \bibitem{EmKu77} A.~Emeryk, W.~Kulpa, {\em The Sorgenfrey line has no connected compactification}, Comment. Math. Univ. Carolinae {\bf18} (1977), no.~3, 483--487. \bibitem{FL98} A.~Fedeli, A.~Le Donne, {\em One-point connectifications of subspaces of the Euclidean line}, Rend. Mat. Appl. (7) {\bf18} (1998), no.~4, 677--682 (1999). 54D05 (54C25) \bibitem{FL99a} A.~Fedeli, A.~Le Donne, {\em Dense embeddings in pathwise connected spaces}, Topology Appl. {\bf96} (1999), no.~1, 15--22. 54D05 (54C25) \bibitem{FL99b} A.~Fedeli, A.~Le Donne, {\em On locally connected connectifications}, Topology Appl. {\bf96} (1999), no.~1, 85--88. 54D05 (54C25) \bibitem{FL99c} A.~Fedeli, A.~Le Donne, {\em An independency result in connectification theory}, Comment. Math. Univ. Carolin. {\bf40} (1999), no.~2, 331--334. 54D05 (03E35 54C25 54D25) \bibitem{FL2000a} A.~Fedeli, A.~Le Donne, {\em Connectifications and open components}, Questions Answers Gen. Topology {\bf18} (2000), no.~1, 41--45. \bibitem{FL2000b} A.~Fedeli, A.~Le Donne, {\em On subconnected spaces}, Questions Answers Gen. Topology {\bf18} (2000), no.~1, 97--102. \bibitem{FL2001} A.~Fedeli, A.~Le Donne, {\em The Sorgenfrey line has a locally pathwise connected connectification}, Proc. Amer. Math. Soc. {\bf129} (2001), no.~1, 311--314. 54D05 (54D35) \bibitem{FL2000c} A.~Fedeli, A.~Le Donne, {\em $\omega$-connectifications and product spaces}, Questions Answers Gen. Topology {\bf18} (2000), no.~2, 283--288. \bibitem{GKL98} G.~Gruenhage, J.~Kulesza, A.~Le Donne, {\em Connectifications of metrizable spaces}, Special volume in memory of Kiiti Morita. Topology Appl. {\bf82} (1998), no.~1-3, 171--179. \bibitem{PW96} J.\,r.~Porter, R.\,G.~Woods, {\em Subspaces of connected spaces}, Topology Appl. {\bf68} (1996), no.~2, 113--131. \bibitem{WW93} S.~Watson, R.\,G.~Wilson, {\em Embeddings in connected spaces}, Houston J. Math. {\bf19} (1993), no.~3, 469--481. \end{thebibliography}