◀ ▲ ▶Branches / Topology / Definition: First and Second Category Sets

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 $X.$

Thank you to the contributors under CC BY-SA 4.0!

Github:

References

Bibliography

1. Steen, L.A.;Seebach J.A.Jr.: "Counterexamples in Topology", Dover Publications, Inc, 1970
2. Jänich, Klaus: "Topologie", Springer, 2001, 7th Edition