A Brief Historical View of Continuum Theory
We explore a few topics in continuum theory from their roots. Specifically, we examine the evolution of the definition of continuum and then restrict most of our attention to one-dimensional continua. Particular attention is paid to indecomposable continua, the fixed point property, hereditary equivalent continua, homogeneous continua, chainable continua and span of continua. in this paper, we give an inverse limit description of an indecomposable circle-like continuum that is homeomorphic to the first example of an indecomposable continuum given by L.E.J. Brouwer in 1910.
W. T. Ingram, "A Brief Historical View of Continuum Theory," Topology and its Applications, Elsevier, Apr 2006.
The definitive version is available at https://doi.org/10.1016/j.topol.2004.08.024
Mathematics and Statistics
Keywords and Phrases
chainable; circle-like; continuum; fixed point property; hereditarily equivalent; homogeneous; indecomposable; span
Article - Journal
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