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Meager Set


A subset E of a topological space S is said to be meager if E is of first category in S, i.e., if E can be written as the countable union of subsets which are nowhere dense in S. The terms "thin set," "meager set," and "first category" are equivalent.


See also

Baire Category Theorem, First Category, Nowhere Dense, Nonmeager Set, Residual Set, Second Category

Portions of this entry contributed by Barnaby Finch

Portions of this entry contributed by Christopher Stover

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References

Morgan, J. C. Point Set Theory. Boca Raton, FL: CRC Press, p. 12, 1989.Rudin, W. Functional Analysis. New York: McGraw-Hill, 1991.

Referenced on Wolfram|Alpha

Meager Set

Cite this as:

Finch, Barnaby; Stover, Christopher; and Weisstein, Eric W. "Meager Set." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MeagerSet.html

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