Inverse Limits and Related Topics

Sergio Macías
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Sergio Macías: Universidad Nacional Autónoma de México, Instituto de Matemáticas

Chapter Chapter 2 in Topics on Continua, 2018, pp 53-111 from Springer

Abstract: Abstract We present basic results about inverse limits and related topics. An excellent treatment of inverse limits, distinct from the one given here, was written by W. Tom Ingram. First, we present some basic results of inverse limits. Then a construction and a characterization of the Cantor set are given using inverse limits. With this technique, it is shown that a compactum is a continuous image of the Cantor set. Next, we show that inverse limits commute with the operation of taking finite products, cones and hyperspaces. We give some properties of chainable continua. We study circularly chainable and P -like continua. We end the chapter presenting several properties of universal maps and AH-essential maps.

Date: 2018
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DOI: 10.1007/978-3-319-90902-8_2

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