In this paper, we investigate some basic properties, especially categorical properties, of monotone determined spaces. For a topology τ , we construct a monotone determined topology m d ( τ ) . The main results are: (1) for a space ( X , τ ) , then m d ( τ ) is the weakest monotone determined topology on X containing τ ; (2) the category Top md of monotone determined spaces with continuous maps is fully co-reflexive in the category Top of all topology spaces with continuous maps; (3) the category Top md is cartesian closed.
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