Connectifications of Finite Products of the Sorgenfrey Line
by
Richard Lawner
University of Kansas

A connectification of a topological space X is a connected space Y in which X is a dense subspace. A space has a Hausdorff compactification iff it is a Tychonoff space. A corresponding characterization of Hausdorff connectifiability has not been found. In 1977, Emeryck and Kulpa showed that the Sorgenfrey line E has a Hausdorff connectification but no regular connectification. This result has been extended to show that every finite product of E fails to have a regular connectification but has a Hausdorff connectification. It has also been shown that every finite product of E has a Urysohn connectification with countable remainder.

Date received: July 8, 1999