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On Chains in H-Closed Topological Pospaces

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Abstract

We study chains in an H-closed topological partially ordered space. We give sufficient conditions for a maximal chain L in an H-closed topological partially ordered space (H-closed topological semilattice) under which L contains a maximal (minimal) element. We also give sufficient conditions for a linearly ordered topological partially ordered space to be H-closed. We prove that a linearly ordered H-closed topological semilattice is an H-closed topological pospace and show that in general, this is not true. We construct an example of an H-closed topological pospace with a non-H-closed maximal chain and give sufficient conditions under which a maximal chain of an H-closed topological pospace is an H-closed topological pospace.

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Authors and Affiliations

  1. Department of Mechanics and Mathematics, Ivan Franko Lviv National University, Universytetska 1, Lviv, 79000, Ukraine

    Oleg Gutik

  2. Institute of Mathematics, Physics and Mechanics, Jadranska 19, Ljubljana, 1000, Slovenia

    Dušan Pagon

  3. Faculty of Natural and Physics, University of Ljubljana, Jadranska 19, Ljubljana, 1000, Slovenia

    Dušan Repovš

Authors
  1. Oleg Gutik
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  2. Dušan Pagon
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  3. Dušan Repovš
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Correspondence to Dušan Repovš.

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Gutik, O., Pagon, D. & Repovš, D. On Chains in H-Closed Topological Pospaces. Order 27, 69–81 (2010). https://doi.org/10.1007/s11083-010-9140-x

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  • DOI: https://doi.org/10.1007/s11083-010-9140-x

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