open-sets

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.