The Effros Metric
The concepts of the Effros metric and the Effros property are extended in such a way that a semigroup of surjective self mappings of a bounded metric space (in place of autohomeomorphism group) is used in the definitions. Relations between the Effros property for and -homogeneity are investigated. Special attention is paid to locally connected continua and the class of all continuous mappings between them. It is shown that local absolute retracts, as well as locally connected curves, have the Effros property for , while 2-dimensional locally connected continua do not have this property. A number of questions are asked.
J. J. Charatonik and W. J. Charatonik, "The Effros Metric," Topology and its Applications, Elsevier, Mar 2001.
The definitive version is available at http://dx.doi.org/10.1016/S0166-8641(99)00203-5
Mathematics and Statistics
Keywords and Phrases
Effros metric; Effros property; continuum; dendrite; homogeneous; locally connected
Article - Journal
© 2001 Elsevier, All rights reserved.