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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
@article{TAC_2015_30_a52,
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/}
}
TY - JOUR AU - G. Bezhanishvili AU - D. Gabelaia AU - M. Jibladze AU - P. J. Morandi TI - Profinite topological spaces JO - Theory and applications of categories PY - 2015 SP - 1841 EP - 1863 VL - 30 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TAC_2015_30_a52/ LA - en ID - TAC_2015_30_a52 ER -
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/