Geodesic
On the Structure of Finite T0 + T5 Spaces
Canadian journal of mathematics, Tome 25 (1973) no. 6, pp. 1148-1158

Voir la notice de l'article provenant de la source Cambridge University Press

The object of this paper is to study some structural aspects of finite T0 + T4 and T0 + T5 spaces in order to establish certain recursion relations that can be used to obtain the number of (labelled as well as unlabelled) T0 + T5 topologies on a finite set.Here, as in [2], a topology J is a T4(T5) space provided for any pair of disjoint closed sets A and B (separated sets A and B = A ∩ closure B = B ∩ closure A = 0) there exist disjoint open sets 0A and 0B J such that A ⊆ 0A and B ⊆ 0B. An almost immediate consequence of these investigations is that the inherent simplicity of the connected T0 + T5 topologies ensures that they are reconstructable. 
Das, Shawpawn Kumar. On the Structure of Finite T0 + T5 Spaces. Canadian journal of mathematics, Tome 25 (1973) no. 6, pp. 1148-1158. doi: 10.4153/CJM-1973-123-1
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[1] 1. Das, Shawpawn Kumar, A partition of finite T0 topologies, Can. J. Math. 25 (1973), 1137–1147. Google Scholar

[2] 2. Gaal, S. A., Point set topology (Academic Press, New York, 1964). Google Scholar

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