All streets, avenues and alleys within the corporate limits of the City which have been laid out, platted and dedicated as required by law by any owner or owners of the land included in such plats and dedications, which have been accepted by the City by special ordinance, or by being worked by the City under the authorization therefor by the City Council, and which have not been vacated, are the streets and avenues and alleys of the City, subject to the power of the Council to open, close, widen, extend and vacate the same as provided by law. (1958 Code, ch. IV, art. 1)