## A lifting theorem on forcing LCS spaces

Lajos Soukup

Denote by the statement that there is an LCS space of height and width . We prove, for each regular cardinal , that if there is a natural'' c.c.c poset such that holds in then there is a natural'' c.c.c poset as well such that holds in for each .

Key words and phrases: locally compact scattered space, superatomic Boolean algebra, cardinal sequence, lifting theorem

2000 Mathematics Subject Classification: 54A25, 06E05, 54G12, 03E20