# Homotopy and “transfer” equivalence

Let $$X,Y$$ be topological spaces and $$f,g:X\to Y$$ be continuous. We say that there is a transfer function from $$f$$ to $$g$$ if there is $$u:Y\to Y$$ such that $$g = u\circ f$$, and we write $$g\leq_t f$$. We say that $$f,g$$ are transfer equivalent if $$g\leq_t f$$ and $$f\leq_t g$$.

What is an example of spaces $$X,Y$$ and continuous functions $$f,g:X\to Y$$ such that $$f, g$$ are homotopic, but not transfer equivalent – and what is an example for continuous functions that are transfer equivalent, but not homotopic?