Geodesic
A Definition of Separation Axiom
Canadian mathematical bulletin, Tome 17 (1974) no. 4, pp. 485-491

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Several separation axioms, defined in terms of continuous functions, were examined by van Est and Freudenthal [3], in 1951. Since that time, a number of new topological properties which were called separation axioms were defined by Aull and Thron [1], and later by Robinson and Wu [2], This paper gives a general definition of separation axiom, defined in terms of continuous functions, and shows that the standard separation axioms, and all but one of these new topological properties, fit this definition. 
Cramer, T. A Definition of Separation Axiom. Canadian mathematical bulletin, Tome 17 (1974) no. 4, pp. 485-491. doi: 10.4153/CMB-1974-086-8
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     title = {A {Definition} of {Separation} {Axiom}},
     journal = {Canadian mathematical bulletin},
     pages = {485--491},
     year = {1974},
     volume = {17},
     number = {4},
     doi = {10.4153/CMB-1974-086-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1974-086-8/}
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