Geodesic
Grothendieck topologies on Chu spaces
Matematičeskie trudy, Tome 11 (2008) no. 2, pp. 159-186.

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We consider the Grothendieck topologies on low semi-lattices, defined by one family, and the corresponding sheaf cohomology. This is a basis to define and study the left and right cohomologies and the left and right dimensions of the Chu spaces. The construction of Chu spaces allows to characterize a large class of quantities, for example, the dimension of a Noether space or the Krull dimension of a ring, the Lebesgue-type dimensions, as well as to compare them with the cohomology dimensions of the corresponding Chu spaces. We prove existence of spectral sequences of the morphisms of the Chu spaces. 
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E. E. Skurikhin; A. G. Sukhonos. Grothendieck topologies on Chu spaces. Matematičeskie trudy, Tome 11 (2008) no. 2, pp. 159-186. http://geodesic.mathdoc.fr/item/MT_2008_11_2_a5/

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