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Definition: First and Second Category Sets
Let $(X,\mathcal O)$ be a topological space. A subset $U\subset X$ is called:
* first category (or meager) in $X$ if it is the union of a countably many nowhere dense subsets of $X,$
* second category in $X$, if it is not first category in $X.$
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References
Bibliography
 Steen, L.A.;Seebach J.A.Jr.: "Counterexamples in Topology", Dover Publications, Inc, 1970
 Jänich, Klaus: "Topologie", Springer, 2001, 7th Edition