A Brief Historical View of Continuum Theory

Author

William Thomas Ingram, Missouri University of Science and TechnologyFollow

Abstract

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.

Recommended Citation

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

Department(s)

Mathematics and Statistics

Keywords and Phrases

chainable; circle-like; continuum; fixed point property; hereditarily equivalent; homogeneous; indecomposable; span

International Standard Serial Number (ISSN)

0166-8641

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2006 Elsevier, All rights reserved.

Publication Date

01 Apr 2006