I. Juhász

Cardinal Functions on Continuous Images

Denote by F(X,f,C) the set of all values taken by the cardinal function f on all continuous images of X that belong to the class C. What is this "image spectrum"? In particular, do lambda< f(X) and X in C imply lambda in F(X,f,C)? These are the questions investigated in this paper, for various choices of f and C. We show e.g. that if X is compact T_2 then F(X,w,T_2)=[omega,w(X)] and if GCH holds then F(X,d,T_2)=[omega,d(x)] as well.

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