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a r t i c l e i n f o a b s t r a c t MSC: primary 54B05 secondary 06B35, 18B30, 54F05, 54B30 Keywords: Algebraic poset Camp Damp Filter-complete base Maximal point space Minimal base Model Scott topology Stone duality T 1 -space Zero-dimensional We show that the T 1 -spaces are precisely the maximal point spaces of conditionally upcomplete algebraic posets with the Scott topology. Moreover, we establish an equivalence between the category of T 1 -spaces with a distinguished base and a certaindoi:10.1016/j.topol.2011.01.014 fatcat:oqbwz6iu7jcxfpoaubg2ljkayi