A (co)homology theory for some preordered topological spaces

Manuel Norman

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arXiv · 2004.10689

A (co)homology theory for some preordered topological spaces

Manuel Norman

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Abstract

The aim of this short note is to develop a (co)homology theory for topological spaces together with the specialisation preorder. A known way to construct such a (co)homology is to define a partial order on the topological space starting from the preorder, and then to consider some (co)homology for the obtained poset; however, we will prove that every topological space with the above preorder consists of two disjoint parts (one called 'poset part', and the other one called 'complementary part', which is not a poset in general): this suggests an improvement of the previous method that also takes into account the poset part, and this is indeed what we will study here.

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Manuel Norman. 2020-04-15. A (co)homology theory for some preordered topological spaces. https://arxiv.org/abs/2004.10689

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