Open Mappings Increasing Order
It is shown that an analog of Whyburn's theorem saying that open mappings do not increase order of a point of locally compact metric spaces is not true if the Menger-Urysohn order is replaced by order in the classical sense. On the other hand, this analog is true, even for a wider class of confluent mappings, under an additional condition that the mapping is light and the domain continuum is hereditarily unicoherent.
J. J. Charatonik and W. J. Charatonik, "Open Mappings Increasing Order," Proceedings of the American Mathematical Society, American Mathematical Society, Jan 1997.
The definitive version is available at http://dx.doi.org/10.1090/S0002-9939-97-04096-3
Mathematics and Statistics
Keywords and Phrases
classical sense; confluent; continuum; dendroid; light; open mapping; order; smooth
Article - Journal
© 1997 American Mathematical Society, All rights reserved.