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Connectedness

★★★★☆Undergraduate

📖Definition

A topological space is connected if it cannot be separated into two disjoint nonempty open sets.

📐Formulas

X ≠ U ∪ V for disjoint nonempty open U, V

Definition of connectedness

✏️Examples

예제 1

Explain why ℝ is connected.

예제 2

Show ℚ is not connected.

Applications

Analysis

Intermediate value theorem

Graph Theory

Connected graphs

🔗Related Documents

Prerequisites

#연결#위상#connected#topology