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F-nodec spaces

2015
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Applied General Topology
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Following Van Douwen, a topological space is said to be nodec if it satisfies one of the following equivalent conditions: (i) every nowhere dense subset of X, is closed; (ii) every nowhere dense subset of X, is closed discrete; (iii) every subset containing a dense open subset is open. This paper deals with a characterization of topological spaces X such that F(X) is a nodec space for some covariant functor F from the category Top to itself. T0, ρ and FH functors are completely studied.

doi:10.4995/agt.2015.3141
fatcat:jwbmw7ec5fgk3iwk5qo3i2c4ya