Difference between revisions of "Compact lattice element"
From Encyclopedia of Mathematics
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| − | An element $a$ of a lattice $L$ for which the condition | + | An element $a$ of a [[complete lattice]] $L$ for which the condition |
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a \le \bigvee_{j \in J} x_j\,,\ \ x_j \in L\,, | a \le \bigvee_{j \in J} x_j\,,\ \ x_j \in L\,, | ||
Revision as of 12:47, 10 January 2015
2020 Mathematics Subject Classification: Primary: 06B23 [MSN][ZBL]
An element $a$ of a complete lattice $L$ for which the condition $$ a \le \bigvee_{j \in J} x_j\,,\ \ x_j \in L\,, $$ implies $$ a \le x_{j_1} \vee \cdots \vee x_{j_k} $$ for some finite subset $\{j_1,\ldots,j_k\} \subset J$.
How to Cite This Entry:
Compact lattice element. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Compact_lattice_element&oldid=36184
Compact lattice element. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Compact_lattice_element&oldid=36184
This article was adapted from an original article by T.S. Fofanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article