Abstract
A useful characterization of closed sets, and a definition of the closure of a set. Definition of a neighborhood. Convergence of a sequence in ℝn. If the sequence does not converge, it diverges. Definition of a Cauchy sequence. Cauchy’s convergence criterion.
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References
Bartle (1982), Marsden and Hoffman (1993), and Rudin (1982) are good references for standard topological results. For correspondences and their properties, see Hildenbrand and Kirman (1976) or Hildenbrand (1974).
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© 2010 Springer-Verlag Berlin Heidelberg
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Sydsæter, K., Strøm, A., Berck, P. (2010). Topology in Euclidean space. In: Economists’ Mathematical Manual. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28518-2_12
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DOI: https://doi.org/10.1007/978-3-540-28518-2_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26088-2
Online ISBN: 978-3-540-28518-2
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