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open-sets

Verify continuity and open set properties using Z3 solver proofs.

3.9k|296|Updated Dec 23, 2025
Search Tags:#mathematics#continuity#topology#proof#z3 solver#open sets
One-click install
npx skills add https://github.com/parcadei/Continuous-Claude-v3 --skill open-sets-parcadei
Or copy as Structured Prompt for Agent▼
Please help me install this Agent Skill.
Skill: open-sets
Source: https://github.com/parcadei/Continuous-Claude-v3/tree/main/.claude/skills/math/topology/open-sets
Command: npx skills add https://github.com/parcadei/Continuous-Claude-v3 --skill open-sets-parcadei

SYSTEM DOCUMENTATION & REQUIREMENTS

💡 This Skill requires z3_solve.py, and includes scripts (resource) and references (resource) components.

What problem does it solve?

This Skill provides structured approaches and automated tools for solving problems related to open sets in topology, particularly concerning continuity and topological properties.

Core Features & Use Cases

  • Continuity Verification: Checks if a function is continuous using topological definitions (preimage of open sets).
  • Open Set Properties: Helps verify if a given set is open in a metric space.
  • Topological Definitions: Provides methods to understand and work with interior, closure, and boundary of sets.
  • Use Case: When proving a function between topological spaces is continuous, use this skill to verify that the preimage of every open set in the codomain is an open set in the domain.

Quick Start

Use the open-sets skill to prove that the preimage of an open set is open.

Frequently Asked Questions about open-sets

High-intent search queries and answers about installing and using this skill.

FAQPage Schema
How do I prove a function is continuous using open sets in topology?▼

To prove continuity using open sets, you verify that the preimage of every open set in the codomain is an open set in the domain, and this Skill automates that verification process using the Z3 solver.

What is the topological definition of interior, closure, and boundary of a set?▼

The interior, closure, and boundary are fundamental topological definitions of sets, and this Skill provides structured methods and formal proof strategies to help you understand and work with these properties.

How do I verify if a given set is open in a metric space?▼

You can verify if a given set is open in a metric space by applying topological definitions and properties, utilizing the Z3 solver provided by this Skill to formally prove the set's openness.

Can I use the Z3 solver for formal proofs of topological concepts?▼

Yes, you can use the Z3 solver for formal proofs of topological concepts, as this Skill utilizes z3_solve.py to automate continuity verification and validate open set properties.

Do I need to provide specific topological space definitions to check continuity?▼

Yes, checking continuity requires defining the topological spaces involved so the Skill can verify that the preimage of every open set in the codomain is an open set in the domain.

What is the best way to automate topological proofs for open set properties?▼

The best way to automate topological proofs for open set properties is using a formal solver like Z3 to logically validate continuity and set openness based on topological definitions.

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