The Representation Theorem on the Category of FTML( $\mathcal{L}$ )

Abstract

AbstractThe theory of \(\mathcal{L}\)–Fuzzy topological molecule lattices is the generalization theory of topological molecule lattices. The characteristic of category of \(\mathcal{L}\)–Fuzzy topological molecule lattices must be given a straightforward description. In this paper, a representation theorem about the category of \(\mathcal{L}\)–Fuzzy topological molecule lattices is proved: The category of \(\mathcal{L}\)–Fuzzy topological molecule lattices is equal to that the category of FSTS(\(\mathcal{L}\)) which consists of \(\mathcal{L}\)–fuzzifying scott topological space and the \(\mathcal{L}\)–fuzzifying continuous mapping of orientation-join preserving and the relation of way-below preserving. Using it as the deduction of this theorem, a representation theorem about the category of topological molecule lattices is obtained.KeywordsCategoryFuzzy topologyLatticeMapping