Abstract
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.
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Russian Text © The Author(s), 2019, published in Sibirskii Matematicheskii Zhurnal, 2019, Vol. 60, No. 3, pp. 578–598.
The authors were supported by the Basic Scientific Research of the Siberian Branch of the Russian Academy of Sciences (Project 0314-2019-0002) and the Russian Foundation for Basic Research (Grant 18-01-00624a).
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Ershov, Y.L., Schwidefsky, M.V. To the Spectral Theory of Partially Ordered Sets. Sib Math J 60, 450–463 (2019). https://doi.org/10.1134/S003744661903008X
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DOI: https://doi.org/10.1134/S003744661903008X