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My work

Given [tex]\epsilon > 0 [/tex]

fix [tex]c\in A [/tex] want f is continuous at c

[tex]|f(x) - f(c) | = |f(x) - f_n(x) + f_n(x) - f(c) | \leq |f(x) - f_n(x) | + |f_n(x) - f(c) | [/tex]

the first absolute value less that epsilon since [tex]f_n [/tex] converges uniformly to f

and since

[tex]f_n(x) [/tex] is continuous at c so there exist [tex]\delta [/tex] such that [tex]|x - c| < \delta [/tex]

then [tex]|f_n(x) - f(c) | < \epsilon [/tex]

Am i right ?