On one-point connectifications

In the first part of this note we explore the relationship between connectibility and cohesiveness, including showing that the concepts do not coincide in the class of totally disconnected spaces. We introduce the concept of strong cohesion which fits between cohesion and connectibility. Several examples demonstrate the sharpness of the obtained results. In the second part of this note we investigate when certain one-point connectifications have the fixed point property. In particular, we prove this property for the canonical one-point connectification of Erdo{combining double acute accent}s space. This result was claimed earlier in the literature but was withdrawn recently. © 2006 Elsevier B.V. All rights reserved.