first-countable space

C1 可数公理

Geometry & Topology · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Other names / variants: first countability

Translation evidence: Literature usage

Meaning in context

A space in which every point has a countable basis of open neighborhoods: every open neighborhood contains a member of that basis.

每一点均有可数开邻域基，即该点的任意开邻域都包含基中的某个成员。

Example

Metric balls B(x,1/n)B(x,1/n) give such a basis at xx.

Usage and distinctions

The basis may depend on the point; this is weaker than a countable basis for the whole topology. C1 is the source's notation.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Anton Petrunin — A minimalist intro to topologyChapter 9E, Comments, printed p. 70 · Checked 2026-10-14

Translation sources

  1. Bao Zhiqiang — Peking University topology syllabus第2周9月26日，主要概念：C_{1} 可数公理 · Checked 2026-10-14
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