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When semimonotone implies monotone
by
Paul Bankston
Marquette University
A mapping between continua is semimonotone if the pre-image of a subcontinuum has a component that both maps onto the subcontinuum and contains the pre-image of the subcontinuum's interior. We show that a continuum is locally connected precisely when every semimonotone mapping onto it is also monotone. Moreover, if a continuum fails to be locally connected, it is the image, under a semimonotone nonmonotone mapping, of a continuum that shares many important properties-e.g., weight, covering dimension-with the original continuum.
Date received: January 15, 2009
Copyright © 2009 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 # caxy-15.