Why does TSP require no repetition of cities? It seems odd to me that the TSP denies the possibility of repeated cities.  The goal of this traveling salesman is to go as fast as possible and visit all of the cities, right?  So what if it is faster to travel through a city you have already been to?
It doesn't matter exactly how you define it because it's just a way of modelling a real-world problem. In TSP, you just have a set of cities and the cost of travelling between each pair of them. That doesn't exclude the possibility that, in the real world situation you're modelling, the best route between B and&nbsp;C might go through&nbsp;A. If that was the case then, yes, the route that is modeled as ABCA in TSP may very well really involve driving through&nbsp;A an extra time on the way from B to&nbsp;C but such detail is abstracted away in the TSP model.