TY - JOUR
AU - Rogers, C. A.
AB - C. A. ROGERS 1. Introduction In its original form (see N. Lusin [4 or 5, p . 156]) Lusin's first separation theorem asserts that, if A and JB are disjoint analytic sets in Euclidean space, then there is a Borel set C with A <= C and C n B = 0 . Recently Z. Frolik [2] has shown j that, in a HausdorfF space, if A is a Souslin set and B is an analytic set disjoint from A, then there is a Borel set C with A <=. C and C r\B = 0 . In this note we give the following refinement of the theorem, giving extra information about the nature of the separating set C. THEOREM. Let Jtf be a class of sets, all Souslin-^ sets, in a Hausdorff space X. If A is a Souslin-JV set and B is an analytic set that does not meet A, then there is a Borelian-Jf set C with A <= C and C r\B = 0 . This theorem has of course the immediate COROLLARY 1. If A is a Souslin-JV set and its complement is analytic, then A is a Borelian-3^ set. A second corollary needs 
TI - Lusin's First Separation Theorem
JF - Journal of the London Mathematical Society
DO - 10.1112/jlms/s2-3.1.103
DA - 1971-01-01
UR - https://www.deepdyve.com/lp/wiley/lusin-s-first-separation-theorem-6Lim7f0Def
SP - 103
EP - 108
VL - s2-3
IS - 1
DP - DeepDyve
ER -