When / is infinite and 6 is a compact element and with an irredundant finite join - decomposition , it is showed that a sufficient and necessary condition that the solution set is nonempty . it is also proved that there exists a minimal solution if the solution set of the equation sup t ( ai , xi ) = b is nonempty 当论域为无限集， b为紧元且有不可约有限并分解时，给出了解集非空的充要条件，证明了如果方程sup _ ( i i ) ( a _ i ， x _ i ) = b有解，则一定存在极小解。
In particular , some properties of the solution set of the equation a 0 x = b ( where " 0 " denotes sup - inf composition ) are given when the domain is an infinite set on lattice [ 0 , 1 ] . prom the coefficients of the equation aqx = 6 , it is showed that a sufficient and necessary condition that the solution set is nonempty and one for existence of an attainable solution or an unattainable solution 特别在[ 0 ， 1 ]格上对无限论域方程a ? x = n (其中“ ? ”表示sup - inf合成)的解集的性质作了讨论，仅从方程的系数出发给出了方程解集非空的充要条件以及存在可达解或不可达解的充要条件。
