I know that a map $f: X \to Y$ is a homotopy equivalence if there exists a map $g:Y \to X$ such that $gf, fg$ are homotopic to the identiy on respective spaces.
But I don't know what is meant by 'induces a homotopy equivalence '.
Can anyone explain the definition and mention important stuffs related to that, so that I can relate and understand better.
I was try to solve the following problem but I don't know how to approach these problems. Is it possible to solve it using covering space theory, or singular homology theory?
Problem(True/Flase) There is a map from $S^2 \times S^2 \to S^2 \vee S^2 \vee S^4$ which induces an homotopy equivalence?
Note I haven't learned CW Complexes and Cohomology Theory. So requesting to not post hints/solutions using that. Thanks