On the existence of connected Hausdorff subtopologies
by
Richard G. Wilson
Universidad Autónoma Metropolitana, Unidad Iztapalapa, México D.F.
Coauthors: Gary Gruenhage, Vladimir Tkachuk

In [1] we have shown that each non-compact second countable regular space has a weaker connected Hausdorff subtopology. Here we extend this result to show that

1) Each disconnected metric space

2) Each disconnected Hausdorff space with a countable network,

3) Each disconnected Hausdorff space with a \sigma-locally finite base and whose weight is a successor cardinal

has a weaker connected Hausdorff subtopology if and only if it is not H-closed.

[1] M. G. Tkacenko, V. V. Tkachuk, V. V. Uspenskij, R. G. Wilson, In quest of weaker connected topologies, Comm. Math. Univ. Carolinae, 1996, 37, no. 4, 825-841.

Date received: June 2, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeu-12.