Fundamental groupoid of Alexandroff space X is naturally isomorphic to localization of its thin specialization-preorder category; regular coverings are represented by morphism-inverting functors extending Minian-Barmak.
Smallest homotopically trivial non-contractible spaces
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abstract
We characterize the homotopically trivial non-contractible topological spaces with the minimum number of points.
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2019 1verdicts
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Regular coverings and fundamental groupoids of Alexandroff spaces
Fundamental groupoid of Alexandroff space X is naturally isomorphic to localization of its thin specialization-preorder category; regular coverings are represented by morphism-inverting functors extending Minian-Barmak.