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Published online by Cambridge University Press: 20 November 2018
L. L. Herrington recently characterized completely Hausdorff-closed topological spaces in terms of arbitrary filterbases and a type of convergence for filterbases called f-convergence [2], Before this, characterizations of these spaces via filterbases was by open filterbases [1]. In this article, we employ Herrington's characterizations to obtain characterizations of completely Hausdorff-closed spaces in terms of projections and in terms of graphs of functions into the spaces; both of these—projections and graphs—are utilized in conjunction with a class S of spaces containing as a subclass the Hausdorff completely normal fully normal spaces to effect the characterizations.