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 | ||
| + | $$ | ||
| + | a \le \bigvee_{j \in J} x_j\,,\ \ x_j \in L\,, | ||
| + | $$ | ||
implies | implies | ||
| − | + | $$ | |
| − | + | a \le x_{j_1} \vee \cdots \vee x_{j_k} | |
| − | + | $$ | |
| − | for some finite subset | + | for some finite subset $\{j_1,\ldots,j_k\} \subset J$. |
Revision as of 12:45, 10 January 2015
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=16139
Compact lattice element. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Compact_lattice_element&oldid=16139
This article was adapted from an original article by T.S. Fofanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article