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Characterization of hereditarily reversible posets

  • Michał Kukieła EMAIL logo
Published/Copyright: August 17, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 3

Abstract

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“

(Communicated by Miroslav Ploščica)

Acknowledgement

The author would like to thank Bernd Schröder for reading a preliminary version of this paper.

References

[1] Alexandroff, P.: Diskrete Räume, Mat. Sbornik 2 (1937), 501–518.Search in Google Scholar

[2] Bonato, A.—Bruhn, H.—Diestel, R.—Sprüssel, P.: Twins of rayless graphs, J. Combin. Theory Ser. B 101 (2011), 60–65.10.1016/j.jctb.2010.10.004Search in Google Scholar

[3] Doyle, P. H.—Hocking, J. G.: Bijectively related spaces. I. Manifolds, Pacific J. Math. 111 (1984), 23–33.10.2140/pjm.1984.111.23Search in Google Scholar

[4] Erné, M.: The ABC of order and topology. In: Category Theory at Work (H. Herrlich, H.-E. Porst, eds.), Heldermann Verlag, Berlin, 1991, pp. 57–83.Search in Google Scholar

[5] Kukieła, M.: Reversible and bijectively-related posets, Order 26 (2009), 119–124.10.1007/s11083-009-9111-2Search in Google Scholar

[6] Rajagopalan, M.—Wilansky, A.: Reversible topological spaces, J. Aust. Math. Soc. 61 (1966), 129–138.10.1017/S1446788700004705Search in Google Scholar

Received: 2013-5-23
Accepted: 2013-12-13
Published Online: 2016-8-17
Published in Print: 2016-6-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0155
Keywords for this article
order preserving bijection; automorphism; hereditarily reversible poset; continuous bijection; homeomorphism; hereditarily reversible topological space

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  1. Research Article
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  3. Research Article
  4. Characterization of hereditarily reversible posets
  5. Research Article
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  7. Research Article
  8. Diophantine equation X4+Y4 = 2(U4 + V4)
  9. Research Article
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  11. Research Article
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  13. Research Article
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  15. Research Article
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  17. Research Article
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  19. Research Article
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