Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6424730 | Topology and its Applications | 2012 | 10 Pages |
Abstract
Every Peano continuum has a strong deformation retract to a deforested continuum, that is, one with no strongly contractible subsets attached at a single point. In a deforested continuum, each point with a one-dimensional neighborhood is either fixed by every self-homotopy of the space, or has a neighborhood which is a locally finite graph. A minimal deformation retract of a continuum (if it exists) is called its core. Every one-dimensional Peano continuum has a unique core, which can be obtained by deforestation. We give examples of planar Peano continua that contain no core but are deforested.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
G. Conner, M. Meilstrup,