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  • 1 Department of Mathematics, Linkoping University, 581 83 Linkoping, Sweden
  • 2 Department of Mathematics, Shimane University, Matsue, Shimane, 690-8504, Japan
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We consider the classes of remainders of locally compact noncompact separable metrizable spaces X in metrizable compactifications. For each integer n≧1 we describe the classes of spaces X additionally having the n-complementation property in the sense of Cain, Jr. Then we show that for each α<ω1 there is a locally compact noncompact separable metrizable space Hα such that is a strictly increasing sequence in the family of all classes .

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