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摘要
In this paper, a new notion of (v-consistent) L (*)-closure L-system is proposed where L is a complete residuated lattice and is a truth stresser on L. The one-to-one correspondence between (v-consistent) L (*)-closure L-systems and (v-consistent) L (*)-closure operators is established. Furthermore, the notion of v-consistent L (*)-closure system is introduced. It is shown that the notion of (v-consistent) L (*)-closure L-system provides an alternative way to characterize (v-consistent) L (*)-closure systems. Finally, the category of (v-consistent) L (*)-closure system spaces is introduced in virtue of the notion of continuous mapping. It is shown that the categories of L (*)-closure L-system spaces, L (*)-closure spaces and L (*)-closure system spaces are isomorphic with each other.
