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Definition: Suppose that f: X -> Y is an injective continuous map, where X and Y are topological spaces. Let Z be the image set f(X), considered as a subspace of Y; then the function f*: X -> Z obtained by restricting the range of f is bijective . If f* happens to be a homemorphism of X with Z, we say that the map f: X -> Y is a topological imbedding, or simply an imbedding, of X in Y.
Source: Topology (second edition) by James R. Munkres