Pathologies in cohomology of non-paracompact Hausdorff spaces
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keywords
cohomologyhausdorffnon-paracompactsheafspaceacyclicadmitsbundles
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We construct a non-paracompact Hausdorff space for which Cech cohomology does not coincide with sheaf cohomology. Moreover, the sheaf of continuous real-valued functions is neither soft nor acyclic, and our space admits non-numerable principal bundles.
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