Open spaces in the subsurface region (<10 mu m) of very low density polyethylene were probed by a monoenergetic positron beam. From measurements of Doppler broadening spectra measurements of the annihilation radiation and the lifetime spectra of positrons as a function of incident positron energy, the size of the open spaces in the region of 0-3 mu m was found to be larger than that in the deeper region. This was attributed to the cooperative motion of large segments of molecules which is activated near the surface. After the freezing in of such motions (below 230 K), although the lineshape parameter S in the bulk was almost constant, S in the region of 0-3 mu m decreased with decreasing temperature. This discrepancy was associated with the presence of the open spaces with an excess content and the resultant contraction of amorphous structure near the surface.