标题： 余层同调 显示英文标题

标题： Cosheaf homology

摘要： 本文从不同角度研究了余层同调：在位点态射下的行为、通过谱序列与 Cech 同调的联系，以及利用超覆盖描述余层同调。证明了在豪斯多夫仿紧空间的情形下，余层同调一般与 Cech 同调同构，并且对于常数余层是同构于形态逆同调的。在 Alexandroff 空间的情形下，包括有限和局部有限空间，余层同调与奇异同调是同构的。 显示英文摘要

摘要： In this paper the cosheaf homology is investigated from different viewpoints: the behavior under site morphisms, connections with Cech homology via spectral sequences, and description of cosheaf homology using hypercoverings. It is proved that in the case of Hausdorff paracompact spaces, the cosheaf homology in general is isomorphic to the Cech homology, and for a constant cosheaf is isomorphic to the shape pro-homology. In the case of Alexandroff spaces, including finite and locally finite spaces, the cosheaf homology is isomorphic to the singular homology.