The homotopy dimension of codiscrete subsets of the 2-sphere

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dc.creatorCannon, J. W.
dc.creatorConner, G. R.
dc.date2006-03-03
dc.date.accessioned2026-07-07T07:06:29Z
dc.date.available2026-07-07T07:06:29Z
dc.descriptionWe characterize those planar Peano continua that are homotopy equivalent to 1-dimensional sets. While many planar Peano continua are not homotopically 1-dimensional, we prove that each has fundamental group that embeds in the fundamental group of a 1-dimensional planar Peano continuum. We leave open the following question: Is a planar Peano continuum homotopically 1- dimensional if its fundamental group is isomorphic with the fundamental group of a 1-dimensional planar Peano continuum?
dc.description18 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/math/0603069
dc.identifierhttp://arxiv.org/abs/math/0603069
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/110043
dc.subjectGeometric Topology
dc.subjectAlgebraic Topology
dc.subject54F50;55M10
dc.titleThe homotopy dimension of codiscrete subsets of the 2-sphere
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