MHB Quick question about continuous mapping

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When f maps E into a metric space Y: (E is subset of metric space X)
Is it eqivalent to say that f is a continuous mapping and that for a subset E of X, to say that for every p element of E, f is continuous at p.?

thank you
 
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Yes. To say that a function (or mapping) is continuous is the same as saying that it is continuous at each point of its domain.
 

Thread 'Apparent counter-example to Cauchy-Goursat theorem (Complex Analysis)'

I posted this question on math-stackexchange but apparently I asked something stupid and I was downvoted. I still don't have an answer to my question so I hope someone in here can help me or at least explain me why I am asking something stupid. I started studying Complex Analysis and came upon the following theorem which is a direct consequence of the Cauchy-Goursat theorem: Let ##f:D\to\mathbb{C}## be an anlytic function over a simply connected region ##D##. If ##a## and ##z## are part of...
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