Continuous mappings

A continuous mapping is a way to connect one set of points (or objects) to another so that small changes in the original result in small changes in the connected points. Think of it like drawing a smooth line—if you slightly move a starting point, the end point moves only slightly as well. In mathematical terms, it means there are no sudden jumps or gaps in the mapping. This concept ensures the transformation preserves a sense of closeness, making the relationship predictable and well-behaved across the entire domain.