“Sidewalk,” as used in the provisions of this title relative to bicycles, shall mean all sidewalks laid out as such by a city, town or village district, or reserved by custom for the use of pedestrians, that are within the compact part of a city, village or district. It shall not include crosswalks, nor footpaths outside the compact part of towns and cities that are worn only by travel and not improved by towns or cities or the abutters, nor any paths or walks that are built for the exclusive use of bicyclists.