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1. Joined or fastened together.
a. Not decomposable into two disjoint nonempty open sets.
b. Having a continuous path between any two points. Used of a curve, set, or surface.
3. Related by family.
4. Logically or intelligibly ordered or presented; coherent: a stroke that left him incapable of connected speech.
5. Associated with or related to others, especially to influential or important people: a photographer who was well connected in the fashion world.