To the Spectral Theory of Partially Ordered Sets

• DOI: 10.1134/s003744661903008x
• Publication Date: 2019-06-13T15:03:22Z
• Authors: Yu. L. Ershov; M. V. Schwidefsky
• Keywords: 0102 computer and information sciences; 0101 mathematics; 01 natural sciences

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.