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- Nerve_of_a_covering abstract "In mathematics, the nerve of an open covering is a construction in topology, of an abstract simplicial complex from an open covering of a topological space X.The notion of nerve was introduced by Pavel Alexandrov.Given an index set I, and open sets Ui contained in X, the nerve N is the set of finite subsets of I defined as follows: a finite set J ⊆ I belongs to N if and only if the intersection of the Ui whose subindices are in J is non-empty. That is, if and only ifObviously, if J belongs to N, then any of its subsets is also in N. Therefore N is an abstract simplicial complex.In general, the complex N need not reflect the topology of X accurately. For example we can cover any n-sphere with two contractible sets U and V, in such a way that N is a 1-simplex. However, if we also insist that the open sets corresponding to every intersection indexed by a set in N is also contractible, the situation changes. This means for instance that a circle covered by three open arcs, intersecting in pairs in one arc, is modelled by a homeomorphic complex, the geometrical realization of N.".
- Nerve_of_a_covering wikiPageID "587678".
- Nerve_of_a_covering wikiPageRevisionID "576106452".
- Nerve_of_a_covering hasPhotoCollection Nerve_of_a_covering.
- Nerve_of_a_covering subject Category:Simplicial_sets.
- Nerve_of_a_covering subject Category:Topology.
- Nerve_of_a_covering type Abstraction100002137.
- Nerve_of_a_covering type Collection107951464.
- Nerve_of_a_covering type Group100031264.
- Nerve_of_a_covering type Set107996689.
- Nerve_of_a_covering type SimplicialSets.
- Nerve_of_a_covering comment "In mathematics, the nerve of an open covering is a construction in topology, of an abstract simplicial complex from an open covering of a topological space X.The notion of nerve was introduced by Pavel Alexandrov.Given an index set I, and open sets Ui contained in X, the nerve N is the set of finite subsets of I defined as follows: a finite set J ⊆ I belongs to N if and only if the intersection of the Ui whose subindices are in J is non-empty.".
- Nerve_of_a_covering label "Nerbo (matematica)".
- Nerve_of_a_covering label "Nerf d'un recouvrement".
- Nerve_of_a_covering label "Nerve of a covering".
- Nerve_of_a_covering label "Нерв покрытия".
- Nerve_of_a_covering label "عصب التغطية المفتوحة".
- Nerve_of_a_covering sameAs Nerf_d'un_recouvrement.
- Nerve_of_a_covering sameAs Nerbo_(matematica).
- Nerve_of_a_covering sameAs m.02stmp.
- Nerve_of_a_covering sameAs Q1424012.
- Nerve_of_a_covering sameAs Q1424012.
- Nerve_of_a_covering sameAs Nerve_of_a_covering.
- Nerve_of_a_covering wasDerivedFrom Nerve_of_a_covering?oldid=576106452.
- Nerve_of_a_covering isPrimaryTopicOf Nerve_of_a_covering.