indiscrete topology

平凡拓扑

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

Other names / variants: trivial topology

Translation evidence: Literature usage

Meaning in context

The topology on a set whose only open subsets are the empty set and the whole set.

在一个集合上，仅规定空集和全集为开集的拓扑。

Example

For $X=\{a,b\}$, $\{\varnothing,X\}$ is the indiscrete topology. Both points are limits of every constant sequence in this topology.

Usage and distinctions

It is the coarsest topology on the set, whereas the discrete topology is the finest. On a set with at least two points it is not Hausdorff.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Michael Fochler — Math 330 - Additional Material§7.1.4, Example 7.6, Indiscrete topology · Checked 2026-10-14
2. Anton Petrunin — A minimalist intro to topologyChapter 2B, Examples, concrete/trivial topology · Checked 2026-10-14

Translation sources

1. Bao Zhiqiang — Peking University topology syllabus第1周9月14日，常用例子：平凡拓扑 · Checked 2026-10-14

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