Jordan Journal of Math. and Statistic, cilt.7, ss.15-28, 2014 (ESCI)
If X is T-3, it is showed that the Fan-Gottesman compactification of X can be embedded into compactification (X* ; k) of X obtaining by a combined approach of nets and open filters. By F-spectral, we mean a topological space X such that the Fan-Gottesman compactification of X is a spectral space. We give necessary and sufficient conditions on X in order to get F-spectral.