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Inverse limits as limits with respect to the Hausdorff metric

Published online by Cambridge University Press:  17 April 2009

Iztok Banič
Iztok Banič
Affiliation:
Department of Mathematics, Faculty of Mechanical Engineering, University of Maribor, Smetanova 17, Maribor 2000, Slovenia, e-mail: iztok.banic@uni-mb.si
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We show that the inverse limit of any inverse sequence of compact metric spaces and surjective bonding maps is in fact the limit of a sequence of homeomorphic copies of the same spaces with respect to the Hausdorff metric.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 75 , Issue 1 , February 2007 , pp. 17 - 22
Copyright
Copyright © Australian Mathematical Society 2007

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