An Introduction to Inverse Limits with Set-Valued Functions

ISBN-13: 9781461444862 / Angielski / Miękka / 2012 / 86 str.

W. T. Ingram

Opis

Inverse limits with set-valued functions are quickly becoming a popular topic of research due to their potential applications in dynamical systems and economics. This brief provides a concise introduction dedicated specifically to such inverse limits. The theory is presented along with detailed examples which form the distinguishing feature of this work. The major differences between the theory of inverse limits with mappings and the theory with set-valued functions are featured prominently in this book in a positive light. The reader is assumed to have taken a senior level course in analysis and a basic course in topology. Advanced undergraduate and graduate students, and researchers working in this area will find this brief useful. ​

Recenzje

From the reviews:

"The present volume, part of the 'Springer Briefs in Mathematics' series, stays focused and eminently accessible to undergraduates, who will find exciting research opportunities spelled out in this concrete and nearly brand new subject. Summing Up: Recommended. Upper-division undergraduates and above." (D. V. Feldman, Choice, Vol. 50 (9), May, 2013)

"The technique of inverse limits is very useful in many areas of mathematics. ... In the present book the emphasis is on inverse limits for set-valued functions ... . An important feature of the book is numerous examples that illustrate the difference between single-valued and set-valued inverse limits. The book is meant as an introduction to the area and should be accessible to advanced undergraduate and graduate students." (S. Mardesic, Mathematical Reviews, March, 2013)

"The book is reader-friendly: definitions, theorems, and proofs are supported by many illustrative examples. This makes this book really stand out and greatly improves its readability, making it accessible also to general readers in mathematics. Advanced undergraduate students, graduate students, and researchers that are working in the area of inverse limits will definitely find the book very useful." (Iztok Banic, Zentralblatt MATH, Vol. 1257, 2013)

Spis treści

​ 1. Basics.- 2. Connectedness.- 3. Mapping verses Set-valued Functions.- 4.  Mapping Theorems.- 5. Dimension.- 6. Problems.–Index.​