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54-XX General topology
54Axx Generalities
54A05 Topological spaces and generalizations (closure spaces, etc.)

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Hausdorff Fréchet closure spaces with maximum topological defect

Riccardo Ghiloni (2002)

Bollettino dell'Unione Matematica Italiana

It is well-known that the topological defect of every Fréchet closure space is less than or equal to the first uncountable ordinal number $ω_{1}$ . In the case of Hausdorff Fréchet closure spaces we obtain some general conditions sufficient so that the topological defect is exactly $ω_{1}$ . Some classical and recent results are deduced from our criterion.