Siberian Mathematical Journal

, Volume 60, Issue 3, pp 450–463 | Cite as

To the Spectral Theory of Partially Ordered Sets

  • Yu. L. ErshovEmail author
  • M. V. SchwidefskyEmail author


We suggest an approach to advance the spectral theory of posets. The validity of the Hofmann-Mislove Theorem is established for posets and a characterization is obtained of the sober topological spaces as spectra of posets with topology. Also we describe the essential completions of topological spaces in terms of spectra of posets with topology. Apart from that, some sufficient conditions are found for two extensions of a topological space to be homeomorphic.


poset ideal sober space spectrum essential completion Hofmann-Mislove theorem 


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© Pleiades Publishing, Inc. 2019

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia
  2. 2.Sobolev Institute of MathematicsNovosibirsk State UniversityNovosibirskRussia

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