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13.
On chains in ▫$H$▫-closed topological pospaces
Gutik, Oleg ; Pagon, Dušan ; Repovš, Dušan, 1954-
Preučujemo verige v ▫$H$▫-zaprtem topološkem delno urejenem prostoru. Podamo zadostne pogoje za maksimalno verigo ▫$L$▫ v ▫$H$▫-zaprtem topološkem delno urejenem prstoru (▫$H$▫-zaprti topološki ...polmreži), pri katerih ▫$L$▫ vsebuje maksimalen (minimalen) element. Podamo tudi zadostne pogoje, pri katerih je linearno urejen topološki delno urejen prostor ▫$H$▫-zaprt. Dokažemo, da je linearno urejena ▫$H$▫-zaprta topološka polmreža ▫$H$▫-zaprt topološki delno urejen prostor in, da to v splošnem ne velja. Konstruiramo primer ▫$H$▫-zaprtega topološkega delno urejenega prostora z nezaprto ▫$H$▫-zaprto maksimalno verigo ter podamo zadostne pogoje, pri katerih je maksimalna veriga ▫$H$▫-zaprtega topološkega delno urejenega prostora ▫$H$▫-zaprt topološki delno urejen prostor.
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