continuous at a point

continuous at a point

[kən¦tin·yə·wəs ad ə ′pȯint]
(mathematics)
A function f is continuous at a point x, if for every sequence {xn } whose limit is x, the sequence f (xn) converges to f (x); in a general topological space, for every neighborhood W of f (x), there is a neighborhood N of x such that f -1(W) is contained in N.
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