Question

Problem 4: Let X and Y be metric spaces, E a subset of X, p a limit point of E in X, and q a point of Y.Consider a function f: E->Y. Prove or disprove the following statements: \text { 1. If for all } x \in X, d y(f(x), q) \leq 10 d_{X}(x, p), \text { then } \lim _{x \rightarrow p} f(x)=q \text {. } \text { 2. If for all } x \in X, d_{Y}(f(x), q) \leq d_{X}(x, p)+\frac{1}{10}, \text { then } \lim _{x \rightarrow p} f(x)=q \text {. }

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