uniform base

Let $X$ be a Hausdorff topological space. A basis for $X$ is said to be a uniform base if for all $x\\in X$ and every neighborhood $U$ of $x$ , only a finite number of the basis sets containing $x$ intersect the complement of $U$ .

For example, in any metric space, the open balls of radius $\\frac{1}{n}$ form a uniform base of $X$ .

Any uniform base of $X$ is a point countable base.

References

1 Steen, Lynn Arthur and Seebach, J. Arthur, Counterexamples in Topology, Dover Books, 1995.

单词	UniformBase
释义	uniform base Let $X$ be a Hausdorff topological space. A basis for $X$ is said to be a uniform base if for all $x\\in X$ and every neighborhood $U$ of $x$ , only a finite number of the basis sets containing $x$ intersect the complement of $U$ . For example, in any metric space, the open balls of radius $\\frac{1}{n}$ form a uniform base of $X$ . Any uniform base of $X$ is a point countable base. References 1 Steen, Lynn Arthur and Seebach, J. Arthur, Counterexamples in Topology, Dover Books, 1995.
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