Connectedness is a key idea in topology and metric spaces that describes whether a topological space can be separated into two components. This video explains the open set definition of connectedness and describes the topologist's sine curve as a non-example that motivates the definition of path-connectedness.
Topology playlist: https://www.youtube.com/playlist?list=PLug5ZIRrShJEGnUPxM1KUVOHkW4kN6QU_
Timestamps:
0:00 connectedness
9:59 path-connectedness
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Music: OcularNebula - The Lopez