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Автор (Фамилия, Имя, Отчество):

Karimov, U.H.

Заглавие:

On nerves of fine coverings

Название издания:

Publicationes Mathematicae Debrecen

Год:

1999

Номер издания:

54/3-4

Ключевые слова:

nerve of a covering, fine basis, compactum, separable metric space

Аннотация:

A basis U of a topological space is said to be fine if the closures of every two of its disjoint elements are disjoint. The following are our main results: (1) Every metric space has a fine open basis; (2) Let X and Y be compact Hausdorff spaces with fine bases U and V, respectively. Suppose that the nerves N(U) and N(V) are simplicialy isomorphic. Then X and Y are homeomorphic; and (3) Let (X1, r1) and (X2, r2) be separable metric spaces without isolated points. Then N(r1) is simplicially isomorphic to N(r2).

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Английский

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