Homotopic maps

Definition
Suppose $$X$$ and $$Y$$ are topological spaces and $$f,g:X \to Y$$ are continuous maps. We say that $$f$$ and $$g$$ are homotopic maps or homotopy-equivalent maps (sometimes denoted $$f \simeq g$$ in symbols) if there is a defining ingredient::homotopy between $$f$$ and $$g$$.