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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Path-lifting for Grothendieck toposes


Author: Ieke Moerdijk
Journal: Proc. Amer. Math. Soc. 102 (1988), 242-248
MSC: Primary 18B25,; Secondary 18F10,54E50
DOI: https://doi.org/10.1090/S0002-9939-1988-0920980-X
Addendum: Proc. Amer. Math. Soc. 125 (1997), 2815-2818.
MathSciNet review: 920980
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Abstract: A general path-lifting theorem, which fails in the context of topological spaces, is shown to hold for toposes, for locales (a slight generalization of topological spaces), and hence for complete separable metric spaces. This result generalizes the known fact that any connected locally connected topos (respectively complete separable metric space) is path-connected.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0920980-X
Article copyright: © Copyright 1988 American Mathematical Society