底基层

The subbase of a topological space is the collection of all open sets with respect to which a given topology is defined.
一个拓扑空间的子基是相对于给定拓扑定义的所有开集的集合。
In order to construct a subspace topology, one needs to define a subbase for the topology first.
为了构造子空间拓扑，首先需要定义拓扑的子基。
The product topology on a Cartesian product of topological spaces can be generated by taking the union of the subbases of each individual space.
在笛卡尔积上的乘积拓扑可以通过取每个个体空间的子基的并来生成。
A subbase for the standard topology on the real line is the set of all open intervals with rational endpoints.
实数线上的标准拓扑的子基是所有有理端点的开区间集合。
The subbase for the Zariski topology on affine space is the set of all algebraic varieties.
关于仿射空间的Zariski拓扑的子基是所有代数簇的集合。
To prove that a certain subset is dense in a topological space, it often suffices to show that it intersects every non-empty member of the subbase.
要证明某个子集在拓扑空间中稠密，通常只需证明它与子基中的每一个非空成员相交即可。
The subbase for the weak topology on a normed vector space consists of all finite intersections of open balls centered at the origin.
泛函向量空间上弱拓扑的子基由所有以原点为中心的开球的有限交组成。
In order to define a quotient topology on a set, one often uses the subbase consisting of all preimages of open sets under the quotient map.
为了在集合上定义商拓扑，通常使用所有商映射下开集的原像组成的子基。
The subbase for the discrete topology on any set is the set of all singleton subsets.
任何集合上的离散拓扑的子基是由所有单例子集组成的集合。
To check if a topological space is Hausdorff, it often suffices to verify that its subbase satisfies a certain separation axiom.
要检查一个拓扑空间是否Hausdorff，通常只需验证其子基满足某个分离公理即可。