topology

topology is a skill for Claude Code, Codex from hamzabellouch/agent-skills. It costs 26 tokens per session (218 once invoked), scanned A, original, MIT.

A mathematics skill guide to topology, the study of properties that remain unchanged when shapes are continuously stretched or deformed. It covers open sets, compactness, connectedness, homotopy, fundamental groups, homology, and cohomology.

In plain words
What is it for?
Use it to construct continuous correspondences, calculate fundamental groups, and apply tools such as van Kampen's theorem and the Mayer–Vietoris sequence.
Why use it?
It helps reason about the global structure of spaces without relying on measurements such as length or angle, while avoiding confusion between different kinds of equivalence.

Skill for Claude CodeCodex

Written for no agent in particular: nothing here depends on one.

Good fit Use it to construct continuous correspondences, calculate fundamental groups, and apply tools such as van Kampen's theorem and the Mayer–Vietoris sequence.

Compare 6 skills from other repositories ↓
Install with agentmods
npx agentmods add skills/hamzabellouch/agent-skills/topology
Install

Getting it into your agent

One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.

Any agent
npx skills add hamzabellouch/agent-skills --skill topology
Clone the repo
git clone --depth 1 https://github.com/hamzabellouch/agent-skills

Made for: Claude Code, Codex.

Wrote this? Show the measurements

A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.

agentmods badge for topology

README.md
[![agentmods](https://agentmods.dev/badge/skills/hamzabellouch/agent-skills/topology/github.svg)](https://agentmods.dev/skills/hamzabellouch/agent-skills/topology)
Your own site
<a href="https://agentmods.dev/skills/hamzabellouch/agent-skills/topology"><img src="https://agentmods.dev/badge/skills/hamzabellouch/agent-skills/topology/github.svg" alt="Measured on agentmods" height="20"></a>

Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.

agentmods 80×15 button for topology

Your own site · 80×15
<a href="https://agentmods.dev/skills/hamzabellouch/agent-skills/topology"><img src="https://agentmods.dev/badge/skills/hamzabellouch/agent-skills/topology.svg" alt="Reviewed on agentmods" width="80" height="20"></a>
Per session 26 Skills are progressive disclosure: only the name and description are preloaded; the body loads when the skill is used.
When invoked 218 The whole file, excluding the scripts and references it only reads on demand.
Security scan A 0 findings. A grade says what 26 rules found in the file — not that it is safe.
Origin original No closer match found in the catalogue.
Token cost

What it costs to keep this loaded

Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.

ModelPer sessionOnce invoked
Fable 5.1 $0.00026 $0.00218
Opus 5.5 $0.00010 $0.00087
Sonnet 5.5 $0.00005 $0.00044
Haiku 4.5 $0.00003 $0.00022

Measured 7d ago against content hash fc0e036b3c7a, method: parsed. Prices are Anthropic first-party input rates as of 2026-10-07, from the pricing page.

Security

Grade A, and why

topology scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 7d ago.

A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.

Nothing flagged

None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.

Math/Geometry_and_Topology/topology/SKILL.md · 38 lines

What it actually says

Topology

Domain

Properties preserved under continuous deformation.

Core Concepts

  • Topological spaces, open/closed sets
  • Continuity, homeomorphism
  • Compactness, connectedness
  • Homotopy, fundamental group
  • Homology, cohomology

Key Methods

  • Constructing homeomorphisms
  • Van Kampen's theorem
  • Mayer–Vietoris sequence
  • Euler characteristic

Canonical Examples

  • ℝ and ℝ² are not homeomorphic.
  • Fundamental group of circle = ℤ.
  • Torus: π₁ = ℤ × ℤ.

Common Pitfalls

  • Confusing homotopy with homeomorphism
  • Assuming all spaces are Hausdorff
  • Ignoring base point in π₁

Real Analysis, Differential Geometry, Category Theory

Files

What ships with it

1 file beside SKILL.md in the same directory: the scripts, references and assets a skill reads on demand. Not counted in the per-session cost; read them before you install if any of them is executable.

Changes

What this file has done since we first saw it

Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.

  1. 7d ago First seen · 38 lines · 26 tokens per session scan A fc0e036b3c7a

Subscribe to this mod's changes

topology is a skill published in the GitHub repository hamzabellouch/agent-skills (8 stars, last pushed today), licensed MIT. It adds 26 tokens to every session and 218 once invoked, about $0.0001 per session on Opus 5.5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-10-10.

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