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A NOTE ON CLOSED DISCRETE SUBSETS OF SEPARABLE (a)-SPACES

 

We show that the existence of a T1 separable space with an un- countable closed discrete subset which satisfies relative versions of property (a) and local compactness implies the existence of small dominating families in the family of functions of ω1 into ω. Considering well-known relation- ships between small dominating families and large cardinals, it follows that if Y is an uncountable closed discrete subset of a T1 separable (a)-space X then there is no way to prove within ZFC that Y satisfies relative local compactness. 

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