Limit Point

A number x such that for all epsilon>0, there exists a member of the set y different from x such that |y-x|<epsilon.

The topological definition of limit point P of A is that P is a point such that every open set around it contains at least one point of A different from P.

See also

Accumulation Point, Closed Set, Open Set

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Jeffreys, H. and Jeffreys, B. S. Methods of Mathematical Physics, 3rd ed. Cambridge, England: Cambridge University Press, pp. 9-10, 1988.Lauwerier, H. Fractals: Endlessly Repeated Geometric Figures. Princeton, NJ: Princeton University Press, pp. 25-26, 1991.Munkres, J. R. Topology: A First Course, 2nd ed. Upper Saddle River, NJ: Prentice-Hall, p. 96 2000.

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Limit Point

Cite this as:

Weisstein, Eric W. "Limit Point." From MathWorld--A Wolfram Web Resource.

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