Abstract
A ladder system L on the set of limit ordinals is defined by iterated ccc forcing. The natural topological space X L derived from L is a locally compact, locally countable scattered space of height 2 which is ↗-normal, is a Morita P-space (and thus, countably metacompact), but the space is not perfect or normal. Then we discuss a number of reasons why such a space cannot exist in ZFC and in fact, in many models.
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