Mayer-Vietoris Sequence
Mayer-Vietoris may refer to: * Mayer–Vietoris axiom * Mayer–Vietoris sequence In mathematics, particularly algebraic topology and homology theory, the Mayer–Vietoris sequence is an algebraic tool to help compute algebraic invariants of topological spaces, known as their homology and cohomology groups. The result is due ... {{mathdab ...
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Mayer–Vietoris Axiom
In mathematics, Brown's representability theorem in homotopy theory gives necessary and sufficient conditions for a contravariant functor ''F'' on the homotopy category ''Hotc'' of pointed connected CW complexes, to the category of sets Set, to be a representable functor. More specifically, we are given :''F'': ''Hotc''op → Set, and there are certain obviously necessary conditions for ''F'' to be of type ''Hom''(—, ''C''), with ''C'' a pointed connected CW-complex that can be deduced from category theory alone. The statement of the substantive part of the theorem is that these necessary conditions are then sufficient. For technical reasons, the theorem is often stated for functors to the category of pointed sets; in other words the sets are also given a base point. Brown representability theorem for CW complexes The representability theorem for CW complexes, due to Edgar H. Brown, is the following. Suppose that: # The functor ''F'' maps coproducts (i.e. wedge sums ...
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