Whitehead theorem

Whitehead's theorem states that for connected topological spaces that are "nice" enough (called CW-complexes), a continuous map that induces isomorphisms in all homotopy groups (which measure shape features like holes) is also a homotopy equivalence—meaning the spaces are essentially the same shape from a topological perspective. In simpler terms, if two such spaces look the same when checking their fundamental features, then they can be deformed into each other without tearing or gluing, confirming they are topologically equivalent.