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# Generic Partial Two-Point Sets Are Extendable

It is shown that under $\ZFC$ almost all planar compacta that meet every line in at most two points are subsets of sets that meet every line in exactly two points. This result was previously obtained by the author jointly with K.~Kunen and J.~van~Mill under the assumption that Martin's Axiom is valid.
 MSC Classifications: 57N05 - Topology of $E^2$, $2$-manifolds