basis for a topology

拓扑基

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

Other names / variants: topological base · base for a topology

Translation evidence: Literature usage

Meaning in context

A family of open subsets such that every open subset is a union of members of that family.

由开集组成的族，使每个开集均可写成该族中若干成员的并。

Example

Intervals with rational endpoints form a basis for the usual topology on R\mathbb R.

Usage and distinctions

A subbasis requires finite intersections before arbitrary unions; a basis does not.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Anton Petrunin — A minimalist intro to topologyChapter 6B, Base, printed p. 37 · Checked 2026-10-14

Translation sources

  1. Bao Zhiqiang — Peking University topology syllabus第2周9月26日，主要概念：拓扑基 · Checked 2026-10-14
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