# meager set

## meager set

[¦mē·gər ′set]
(mathematics)
A set that is a countable union of nowhere-dense sets. Also known as set of first category.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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A (FSTS) (U, E, [psi]) is called fuzzy soft meager or (fuzzy soft first category) space if the (FSS) [bar.E] is a fuzzy soft meager set in (U, E, [psi]).
Assume [F.sub.A] is a fuzzy soft meager set in (U, E, [psi]).
Let [F.sub.A] be a fuzzy soft meager set in (U, E, [psi]).
If [F.sub.A] is a fuzzy soft dense and fuzzy soft [delta]-set in a (FSTS) (U, E, [psi]), then [F.sub.A.sup.c] is a fuzzy soft meager set in (U, E, [psi]).
Hence, [F.sub.A.sup.c] is a fuzzy soft meager set in (U, E, [psi]).
Since [F.sub.A] is a fuzzy soft dense and fuzzy soft [delta]-set in (U, E, [psi]), by Proposition 31, we have that [F.sub.A.sup.c] is a fuzzy soft meager set in (U, E, [psi]) and hence [F.sub.A] is a fuzzy soft residual set in (U,E, [psi]).
Therefore, [([T.sup.1.sub.E]).sup.c] is a fuzzy soft meager set in (U, E, [psi]).
If the (FSTS) (U, E, [psi]) is a fuzzy soft submaximal space and if [F.sub.A] is a fuzzy soft [sigma]-meager set in (U, E, [psi]), then [F.sub.A] is a fuzzy soft meager set in (U, E, [psi]).
Therefore, [mathematical expression not reproducible] is a fuzzy soft meager set in (U, E, [psi]).
Then [C.sub.n] is coanalytic and hence has the Baire property [Ke, 21.6], which means that [C.sub.n] coincides with an open subset Un of W modulo some meager set. The latter means that the symmetric difference [U.sub.n] [DELTA][C.sub.n] is meager (i.e., is of the first Baire category) in W.
For Temkin and many like him inside and outside the Soviet Union, the Red Army--and for that matter, the Communist Party, however fundamentally flawed--represented the last, best hope in a meager set of imperfect alternatives, and the only one that promised protection and a realistic chance of survival.
No more than a Reader's Digest precis of Barrie's tale with a few contemporary touches, it's theatrically impoverished, running less than 80 minutes with a east of 12, two meager sets and far too many lengthy between-scenes blackouts.

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