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The Tarski–Kantorovitch prinicple and the theory of iterated function systems

Published online by Cambridge University Press:  17 April 2009

Jacek Jachymski ,
Leslaw Gajek  and
Piotr Pokarowski
Jacek Jachymski
Affiliation:
Institute of Mathematics, Technical University of Łódź, Al. Politechniki 11, 90-924 Łódź, Poland e-mail: [email protected]@ck-sg.p.lodz.pl
Leslaw Gajek
Affiliation:
Institute of Mathematics, Technical University of Łódź, Al. Politechniki 11, 90-924 Łódź, Poland e-mail: [email protected]@ck-sg.p.lodz.pl
Piotr Pokarowski
Affiliation:
Institute of Applied Mathematics and Mechanics, Warsaw University, Banacha 2, 02-097 Warsaw, Poland e-mail: [email protected]
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Abstract

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We show how some results of the theory of iterated function systems can be derived from the Tarski–Kantorovitch fixed–point principle for maps on partialy ordered sets. In particular, this principle yields, without using the Hausdorff metric, the Hutchinson–Barnsley theorem with the only restriction that a metric space considered has the Heine–Borel property. As a by–product, we also obtain some new characterisations of continuity of maps on countably compact and sequential spaces.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 61 , Issue 2 , April 2000 , pp. 247 - 261
Copyright
Copyright © Australian Mathematical Society 2000

References

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