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LUZIN GAPS ARE NOT COUNTABLY PARACOMPACT

 

In this paper we show that if an almost disjoint family A is a Luzin gap then the corresponding space Ψ(A) is not countably paracompact. This answers a Question of the third author, posed in Vol. 25 of this journal, about the value of the cardinal invariant ncp ([7]). By going a little further, we also show that countably paracompact Ψ-spaces of size ω1 violate the condition of being Luzin gaps in a very strong way. 

Docentes Autores: 
Outros autores: 
Charles J. G. Morgan, Michael Hrusák
Data: 
2012