Geodesic
Profinite topological spaces
Theory and applications of categories, Tome 30 (2015), pp. 1841-1863.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

It is well known that profinite $T_0$-spaces are exactly the spectral spaces. We generalize this result to the category of all topological spaces by showing that the following conditions are equivalent:
(1) $(X,\tau)$ is a profinite topological space.
(2) The $T_0$-reflection of $(X,\tau)$ is a profinite $T_0$-space.
(3) $(X,\tau)$ is a quasi spectral space.
(4) $(X,\tau)$ admits a stronger Stone topology $\pi$ such that $(X, \tau,\pi)$ is a bitopological quasi spectral space
Publié le :
Classification : 18B30, 18A30, 54E55, 54F05, 06E15
Keywords: Profinite space, spectral space, stably compact space, bitopological space, ordered topological space, Priestley space 
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     author = {G. Bezhanishvili and D. Gabelaia and M. Jibladze and P. J. Morandi},
     title = {Profinite topological spaces},
     journal = {Theory and applications of categories},
     pages = {1841--1863},
     publisher = {mathdoc},
     volume = {30},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2015_30_a52/}
}
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G. Bezhanishvili; D. Gabelaia; M. Jibladze; P. J. Morandi. Profinite topological spaces. Theory and applications of categories, Tome 30 (2015), pp. 1841-1863. http://geodesic.mathdoc.fr/item/TAC_2015_30_a52/