continuous at a point

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continuous at a point [kən¦tin·yə·wəs ad ə ′pȯint]

(mathematics)

A functionfis continuous at a pointx, if for every sequence {x_n} whose limit isx,the sequencef(x_n) converges tof(x); in a general topological space, for every neighborhoodWoff(x), there is a neighborhoodNofxsuch thatf^-1(W) is contained inN.

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