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词汇 Nowhere dense set
分类 英语词汇 英语翻译词典
释义

Nowhere dense set

中文百科

无处稠密集

拓扑空间(X,τ),A⊆X,称A是无处稠密的(亦称稀疏的,或称A为无处稠密集稀疏集),当且仅当A的闭包的内部是空集。

英语百科

Nowhere dense set 无处稠密集

In mathematics, a nowhere dense set in a topological space is a set whose closure has empty interior. In a very loose sense, it is a set whose elements are not tightly clustered (as defined by the topology on the space) anywhere. The order of operations is important. For example, the set of rational numbers, as a subset of R, has the property that the interior has an empty closure, but it is not nowhere dense; in fact it is dense in R. Equivalently, a nowhere dense set is a set that is not dense in any nonempty open set.

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