Physical Sciences and Mathematics Commons^™

Cardinal Invariants Concerning Extendable And Peripherally Continuous Functions, Krzysztof Ciesielski

Faculty & Staff Scholarship

Let F be a family of real functions, F ⊆ R R . In the paper we will examine the following question. For which families F ⊆ R R does there exist g : R → R such that f + g ∈ F for all f ∈ F? More precisely, we will study a cardinal function A(F) defined as the smallest cardinality of a family F ⊆ R R for which there is no such g. We will prove that A(Ext) = A(PR) = c + and A(PC) = 2c , where Ext, PR and PC stand for the …