TY - JOUR

T1 - To the Spectral Theory of Partially Ordered Sets

AU - Ershov, Yu L.

AU - Schwidefsky, M. V.

PY - 2019/5/1

Y1 - 2019/5/1

N2 - 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.

AB - 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.

KW - essential completion

KW - Hofmann-Mislove theorem

KW - ideal

KW - poset

KW - sober space

KW - spectrum

UR - http://www.scopus.com/inward/record.url?scp=85067308553&partnerID=8YFLogxK

U2 - 10.1134/S003744661903008X

DO - 10.1134/S003744661903008X

M3 - Article

AN - SCOPUS:85067308553

VL - 60

SP - 450

EP - 463

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 3

ER -