Radial profiles of the space potential are measured at the n/m = 1/1 magnetic island produced by external perturbation coils in the Large Helical Device (LHD). Both the temperature and space potential are flat inside the magnetic island, and the large radial electric field shear appears at the boundary of the magnetic island because the radial electric field is zero inside the magnetic island. However, when the width of the magnetic island becomes large, the space potential profile becomes peaked because of the convective flow along the magnetic flux surface inside the magnetic island around the O point. The appearance of the convective flow suggests that the perpendicular viscosity is significantly reduced inside the magnetic island. The perturbation transport study using the cold-pulse propagation is a useful tool to study the transport inside the magnetic island, where the temperature gradient is zero in the steady state. Inside the magnetic island, the cold-pulse propagates slowly from the boundary toward the center, and radial profiles of the delay time are peaked at the magnetic island. The large delay time (slow pulse propagation) indicates that the thermal diffusivity is even small inside the magnetic island. These experimental results indicate that the heat and momentum transport are significantly improved inside the magnetic island although the temperature and flow gradients are zero due to the lack of heat and momentum fluxes.