A subset of a topological space is said to be meager if is of first category in , i.e., if can be written as the countable union of subsets which are nowhere dense in . The terms "thin set," "meager set," and "first category" are equivalent.
Meager Set
See also
Baire Category Theorem, First Category, Nowhere Dense, Nonmeager Set, Residual Set, Second CategoryPortions 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 SetCite this as:
Finch, Barnaby; Stover, Christopher; and Weisstein, Eric W. "Meager Set." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MeagerSet.html