singular simplex

奇异单形

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

Translation evidence: Community usage

Meaning in context

A continuous map from the standard n-simplex with ordered vertices into a topological space, for some nonnegative integer n.

从具有有序顶点的标准 nn 维单形到拓扑空间的连续映射，n≥0n\geq0。

Example

A constant map Δ2→{p}⊆X\Delta^2\to\{p\}\subseteq X is a singular two-simplex.

Usage and distinctions

The map need not be injective; its image need not look like a geometric simplex.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Allen Hatcher — Algebraic Topology§2.1, Singular Homology, printed p. 108 · Checked 2026-10-14

Translation sources

  1. FDU Math — 现代几何学导论, student-compiled original notes§4.3 奇异同调，Definition 奇异单形，printed p. 73 · Checked 2026-10-14
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