Council action to vacate, discontinue, or abolish any highway, street, lane, alley, or other public place or part thereof, shall be by resolution. After the introduction of such resolution, and before its final adoption, the Council shall appoint a time when it shall meet and hear objections thereto. Notice of the time, place, and purpose of such meeting shall be published, either separately or as part of the proceedings of the Council. Objections to any such proposed resolution may be filed with the Clerk in writing, and, if any objections shall be filed, the highway, street, lane, alley, or other public place, or part thereof, shall not be vacated, discontinued, or abolished except by a vote of five of the members of the Council.