Improving the Mathematical Definition of Scale Symbol,Non-scale Symbol and Semi-scale Symbol in the Map

The mapping objects in the three-dimensional space need being projected on S surface of earth-ellipsoid,so there is the mapping f:X→S from three-dimensional space X to the S surface of earth-ellipsoid.It is the premise of showing x on map for the attribute,measurement,shape,etc.characters of x and its mapping f(x) on S are known and undersdood by the cartographer,so there is the mapping g:S→Y from the S surface of earth-ellipsiod to the body cognition construction Y.The idea model of x in Y gf(x) may show on two-dimensional plane Z,so there is the mapping q:Y→Z from the body(idea) construction Y to the two-dimensional plane Z.According to the theorem non-deteriorate inter-regional belonging to the equipollence set,we know that the f,g,q are bijective,this makes x,f(x),gf(x) and qgf(x) corresponding one to one.It decides the map symbol qgf(x) belonging to the scale symbol or non-scale symbol or semi-scale symbol respectively for the f(x) and qgf(x) with the map scale 1∶M are related,aren't related or semi-related.