Topic: Path-Connected Spaces and Components

Why Path-Connected Spaces Are Connected

Why Paths Cannot Join the Sine Curve Branches

The Topologist’s Sine Curve as a Subspace

Reversing Paths and Concatenating Segments

Reparametrizing Paths Without Changing Their Trace

Paths Through a Common Point in Star-Shaped Sets

Paths Constrained to a Subspace

Paths in Convex Subsets of Euclidean Space

Paths as Continuous Maps From an Interval

Path-Connectedness in Standard Examples