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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

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Volume 66, Issue 3


Characterization of hereditarily reversible posets

Michał Kukieła
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  • Faculty of Mathematics and Computer Science Nicolaus Copernicus University ul. Chopina 12/18 87-100 Toruń POLAND
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Published Online: 2016-08-17 | DOI: https://doi.org/10.1515/ms-2015-0155


A poset P is called reversible if every order preserving bijective self map of P is an order automorphism. P is called hereditarily reversible if every subposet of P is reversible. We give a complete characterization of hereditarily reversible posets in terms of forbidden subsets. A similar result is stated also for preordered sets. As a corollary we extend the list of known examples of hereditarily reversible topological spaces.

MSC 2010: Primary 06A06; Secondary 54F99

Key words: order preserving bijection; automorphism; hereditarily reversible poset; continuous bijection; homeomorphism; hereditarily reversible topological space

During the preparation of this paper the author has been supported by the joint PhD programme “Środowiskowe Studia Doktoranckie z Nauk Matematycznych“


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About the article

Received: 2013-05-23

Accepted: 2013-12-13

Published Online: 2016-08-17

Published in Print: 2016-06-01

Citation Information: Mathematica Slovaca, Volume 66, Issue 3, Pages 539–544, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2015-0155.

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