Abstract
Function is a popular and important part of Mathematics. This paper will mainly focus on the continuous functions and will discuss two separate results. If a continuous function from reals to reals is injective when restricted to a set A, then can we extended the property of injection from the set A to the whole real line? We will study what kind of set A will let this happen and what will not. The second part will study the measure of images of sets in Rn.
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