Before revision:  Based on the hedging dualities, we also get the duality for the utility maximization involving semi-static trading strategies .
After revision:  Based on the hedging dualities, we also get the duality for the utility maximization . In the second part of the paper, we consider the market which admits non-dominated model uncertainty. We first establish the hedging result, and then using the hedging duality we further get the FTAP. Due to the technical difficulty stemming from the non-dominancy of the probability measure set, we use a discretization technique and apply the minimax theorem .