Geodesic
Characterizations of Completely Hausdorff-closed Spaces Via Graphs and Projections
Canadian journal of mathematics, Tome 30 (1978) no. 1, pp. 154-160

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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. 
Joseph, James E. Characterizations of Completely Hausdorff-closed Spaces Via Graphs and Projections. Canadian journal of mathematics, Tome 30 (1978) no. 1, pp. 154-160. doi: 10.4153/CJM-1978-013-1
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