I'm reading section 2.7 (Fundamental Group of the Circle) of the book Algebraic Topology by Tom Dieck. The section mentions the term "topological groupoid" but I cannot find the definition in previous sections.
I tried to think of it as a similar term to "topological group" but I'm still having trouble reading the proof of $\pi_1(S^1,*)\cong \mathbb Z$ without an exact definition and a motivation.
Could anyone please give some clue on how one motivate the definition and why the book uses the term without a definition? (I personally do not think it is an elementary definition that can be omitted.)