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A brief historical view of continuum theory. (English) Zbl 1089.54001

Summary: 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.

MSC:

54-03 History of general topology
54F15 Continua and generalizations
01-02 Research exposition (monographs, survey articles) pertaining to history and biography
01A60 History of mathematics in the 20th century
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