L-余闭包系统的确定

Determinination of L-coclosure systems

运用类比和一般化思想研究了L-余闭包系统的确定问题.给出由L-强闭包算子、L-强内部算子以及L-N-强导算子确定L-余闭包系统的具体方法.证明了(SC(X,L),)(X上的L-强闭包算子的全体)(resp.,(SI(X,L),)(X上的L-强内部算子的全体))是与(SF(X,L),)(X上的L-余闭包系统的全体)同构的完备格,且(SD(X,L),)(X上的L-N-导算子的全体)与(SF*(X,L),)(X上的有良闭包的L-余闭包系统的全体)之间存在序同构映射.

Determinination of L-coclosure systems is studied by using the idea of analogy and generalization.Some specific techniques to determininate L-coclosure systems by L-strong closure operator,Lstrong interior operator and L-N-strong derived operator are given.It is proved that SC（X,L）（the set of all L-strong closure operators on X）（resp.,SI（X,L）（the set of all L-strong interior operators on X））and SF（X,L）（the set of all L-co-closure systems on X）are isomorphic complete lattices,and there is an order isomorphic mapping between（SD（X,L）,）（the set of all L N-strong derived operators on X）and（SF＊（X,L）,）（the set of all L-co-closure systems which have nice closure on X）.