Geodesic
Matrix Characterizations of Topological Properties
Canadian mathematical bulletin, Tome 11 (1968) no. 1, pp. 95-105

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DOI

In [S], H. Sharp characterizes each topology on a finite set S = {s1, s2,...sn} with a n×n zero-one matrix T = (tij) where tij=1 if and only if . In this paper we seek matrix characterizations of certain topological properties of finite spaces. Such characterizations will provide purely mechanical ways of determining if a space has a certain topological property. 
Bonnett, D.A.; Porter, J.R. Matrix Characterizations of Topological Properties. Canadian mathematical bulletin, Tome 11 (1968) no. 1, pp. 95-105. doi: 10.4153/CMB-1968-013-9
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     title = {Matrix {Characterizations} of {Topological} {Properties}},
     journal = {Canadian mathematical bulletin},
     pages = {95--105},
     year = {1968},
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     number = {1},
     doi = {10.4153/CMB-1968-013-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1968-013-9/}
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