diff --git a/spaces/S000147/README.md b/spaces/S000147/README.md deleted file mode 100644 index e17168283b..0000000000 --- a/spaces/S000147/README.md +++ /dev/null @@ -1,23 +0,0 @@ ---- -uid: S000147 -name: (CH) A Luzin subset of the reals (The special Lusin set $L$) -aliases: - - Lusin set -ambiguous_construction: true -# additional_axioms: CH -refs: - - zb: 0389.54004 - name: Luzin spaces (K. Kunen) - - doi: 10.1016/S0166-8641(96)00075-2 - name: The combinatorics of open covers II (Just et al) ---- - -An uncountable subset of the reals such that its intersection with -every nowhere dense subset of the reals (equivalently, -every meager subset of the reals) is countable. -For background information, see the article {{zb:0389.54004}}, available at the [Topology Proceedings webpage](https://topology.nipissingu.ca/tp/reprints/v01/tp01021s.pdf). - -Note that the construction of such a set requires additional axioms beyond $ZFC$. - -Here we use the $CH$ construction from Lemma 2.6 of {{doi:10.1016/S0166-8641(96)00075-2}} -in order to guarantee the failure of {P150}. \ No newline at end of file diff --git a/spaces/S000147/properties/P000017.md b/spaces/S000147/properties/P000017.md deleted file mode 100644 index 0da10600ba..0000000000 --- a/spaces/S000147/properties/P000017.md +++ /dev/null @@ -1,10 +0,0 @@ ---- -space: S000147 -property: P000017 -value: false -refs: -- mathse: 4744210 - name: Why can't a Lusin set be sigma-compact? ---- - -Shown in {{mathse:4744210}}. diff --git a/spaces/S000147/properties/P000046.md b/spaces/S000147/properties/P000046.md deleted file mode 100644 index 59af2bdb2f..0000000000 --- a/spaces/S000147/properties/P000046.md +++ /dev/null @@ -1,9 +0,0 @@ ---- -space: S000147 -property: P000046 -value: true ---- - -Assume there are $a,b\in X$ with $a