Preservation of Maps

Preservation of maps refers to the idea that certain mathematical transformations or functions maintain the fundamental structure of a map's features. For example, in geometry, a transformation preserves distances (isometry) if a map keeps the size and shape of objects unchanged, like a perfect stretching or rotating. In topology, a transformation preserves properties like connectedness or continuity, meaning the overall form remains intact even if the shape is stretched or bent. Essentially, preserving a map means the key relationships and features stay consistent under the transformation, ensuring the core structure is unchanged.