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Compact lattice element

From Encyclopedia of Mathematics
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An element $a$ of a 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
This article was adapted from an original article by T.S. Fofanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article