Topic: Connectedness Applications

Why the Circle Cannot Embed in the Line

The One-Dimensional Borsuk-Ulam Theorem

The Fixed-Point Theorem for Interval Maps

The Fixed-Point Sign Test on an Interval

Separating Sets and Multi-Point Deletion

Fixed Points Under Endpoint Conditions

False Claims About Fixed Points

Cut-Point Structure Under Homeomorphisms

Cut Vertices in Finite Graphs

Cut-Point Profiles of Lines, Intervals, and Circles