Published Date
Topology and its Applications
15 September 2012, Vol.159(15):3253–3262, doi:10.1016/j.topol.2012.07.001
Open Access, Creative Commons license, Funding information
Author
M. Meilstrup b,,
Peano continua
Homotopy equivalence
Reduced forms
One-dimensional
Deformation retract
For further details log on website :
http://www.sciencedirect.com/science/article/pii/S0166864112002799
Topology and its Applications
15 September 2012, Vol.159(15):3253–3262, doi:10.1016/j.topol.2012.07.001
Open Access, Creative Commons license, Funding information
Author
Received 18 May 2011. Revised 27 June 2012. Accepted 2 July 2012. Available online 17 July 2012.
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.
MSC
- 55P10
- 57M99
Keywords
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- ☆The first author would like to thank the Fulbright Foundation and the Ad Futura agency, and both authors would like to thank Brigham Young University, the University of Ljubljana, and the University of Leoben for their support. This research was supported by the Austrian Science Foundation (FWF), project S9610, which is part of the national research network FWF-S96 “Analytic combinatorics and probabilistic number theory.”
- ⁎ Corresponding author.
For further details log on website :
http://www.sciencedirect.com/science/article/pii/S0166864112002799
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