MHB Quick question about continuous mapping

[arturo_026]

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

 

[Opalg]

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.