We recall that a topological space Y is called a Hausdorff space if its diagonal Δy is closed in Y x Y. An equivalent formulation of this concept is provided by the following characterization: a topological space Y is a Hausdorff space if for every topological space X and subset M of X, whenever two continuous functions f, g: X → Y agree on M, they must also agree on the topological closure of M.
KeywordsAbelian Group Topological Space Closure Operator Hausdorff Space Torsion Theory
Unable to display preview. Download preview PDF.