Nerve of a covering

In topology, the nerve of an open covering is a construction 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 U_i contained in X, the nerve N is the set of finite subsets of I defined as follows:

单词	Nerve of a covering
释义	Nerve of a covering 英语百科 Nerve of a covering In topology, the nerve of an open covering is a construction 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 U_i contained in X, the nerve N is the set of finite subsets of I defined as follows:
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