Approximate maps characterizing injectivity and surjectivity of maps

Sa？etak In the theory of inverse systems, in order to study the properties of a space X or a map f: X → Y between spaces, one expands X to an inverse system X or expands f to a map f: X → Y between the inverse systems, and then work on X or f. In this paper, we define approximate injectivity (resp., surjectivity) for approximate maps, and show that a map f: X → Y between compact metric spaces is injective (resp., surjective) if and only if any approximate map f