ITES2001 - Fourth Italian-Spanish Conference on
GENERAL TOPOLOGY AND ITS APPLICATIONS
Bressanone, 27-30 June 2001

Dense embeddings in ( pathwise ) connected spaces :
results and open problems

Attilio Le Donne
Università di Roma «La Sapienza», Italy

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}


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