Convergence of Sets in Variable Spaces

  • Peter I. Kogut
  • Günter R. Leugering
Part of the Systems & Control: Foundations & Applications book series (SCFA)


The objective of this chapter is to give a presentation of the mathematical construction and tools that can be used to study problems for which the knowledge of “the limit set” in some appropriate sense is important. We discuss different analytical frameworks and concepts that can be formed on the basis of set convergence in fixed and varying spaces. In this context, we introduce different notions of limits for sequences of nonempty sets and give some applications to the theory of thin periodic and reticulated structures.


Characteristic Function Open Subset Weak Convergence Variable Space Local Chart 
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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Faculty of Mathematics and Mechanics, Department of Differential EquationsOles Honchar Dnipropetrovsk National UniversityDnipropetrovskUkraine
  2. 2.Department of Mathematics, Chair of Applied Mathematics IIFriedrich-Alexander Universität Erlangen-NürnbergErlangenGermany

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