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Sibirskii Matematicheskii Zhurnal, 2019, Volume 60, Number 3, Pages 578–598
DOI: https://doi.org/10.33048/smzh.2019.60.308 (Mi smj3096) 		 
This article is cited in 2 scientific papers (total in 2 papers)

To the spectral theory of partially ordered sets

Yu. L. Ershova, M. V. Schwidefskyba

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
Full-text PDF (399 kB) Citations (2)
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DOI: https://doi.org/10.33048/smzh.2019.60.308
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.
Keywords: poset, ideal, sober space, spectrum, essential completion, Hofmann–Mislove theorem.
Funding agency Grant number
Siberian Branch of Russian Academy of Sciences 0314-2019-0002
Russian Foundation for Basic Research 18-01-00624_a
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).
Received: 28.01.2018
Revised: 06.03.2019
Accepted: 12.03.2019
English version:
Siberian Mathematical Journal, 2019, Volume 60, Issue 3, Pages 450–463
DOI: https://doi.org/10.1134/S003744661903008X
Bibliographic databases:
Document Type: Article
UDC: 515.125
Language: Russian
Citation: Yu. L. Ershov, M. V. Schwidefsky, “To the spectral theory of partially ordered sets”, Sibirsk. Mat. Zh., 60:3 (2019), 578–598; Siberian Math. J., 60:3 (2019), 450–463
Citation in format AMSBIB
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    		Сибирский математический журнал Siberian Mathematical Journal
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