On cardinal sequences of LCS spaces

If α   is an ordinal, we denote by C(α)C(α) the class of all cardinal sequences of length α associated with locally compact scattered spaces (its precise definition is given in Section 1). In this paper, we present a general construction of locally compact scattered spaces with a large top. As consequences of this construction we obtain the following results:(1)If κ is a singular cardinal of cofinality ω  , then 〈κ〉κ〈⌢κω〉∈C(κ+1).(2)If κ   is an inaccessible cardinal, then 〈κ〉κ〈⌢κκ〉∈C(κ+1).(3)If GCH holds, then for any infinite cardinal κ   we have 〈κ〉κ〈⌢κcf(κ)〉∈C(κ+1).Also, we prove that if κ is a singular cardinal of cofinality ω, then for every cardinal λ   such that κ<λ≤κωκ<λ≤κω we have that 〈κ〉κ⌢〈λ〉ω2∈C(κ+ω2).