View source for Disjunctive complement

''of a set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033270/d0332701.png" />''

The set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033270/d0332702.png" /> of all elements <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033270/d0332703.png" /> of a [[Vector lattice|vector lattice]] <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033270/d0332704.png" /> which are disjunctive with the set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033270/d0332705.png" /> (cf. [[Disjunctive elements|Disjunctive elements]]). For any <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033270/d0332706.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033270/d0332707.png" />; moreover, if <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033270/d0332708.png" /> is a conditionally-complete vector lattice (cf. [[Conditionally-complete lattice|Conditionally-complete lattice]]), then <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033270/d0332709.png" /> is the smallest component of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033270/d03327010.png" /> containing <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033270/d03327011.png" />.