We argue that the heliopause, a boundary that separates the solar wind and the plasma of the Local Interstellar Medium (LISM), can be explored remotely, from 1 AU, by detecting solar extreme-ultraviolet (EUV) radiation reflected by the heliospheric interface region. The measurements of the solar EUV radiation echoes from the heliopause would map the heliopause and provide important insight into the LISM parameters. Heliopause mapping can be done in the oxygen O+ resonance line (83.4 nm). We show that the expected heliopause brightness is higher than the expected major source of the background line radiation, viz. the glow of the solar wind O+ pickup ions and discuss a way to remotely establish the ionization state of the LISM and to probe the LISM interstellar magnetic field. ¿ 1998 American Geophysical Union