Cardinal Invariants concerning Bounded Families of Extendable and Almost Continuous Functions
نویسندگان
چکیده
In this paper we introduce and examine a cardinal invariant Ab closely connected to the addition of bounded functions from R to R. It is analogous to the invariant A defined earlier for arbitrary functions by T. Natkaniec. In particular, it is proved that each bounded function can be written as the sum of two bounded almost continuous functions, and an example is given that there is a bounded function which cannot be expressed as the sum of two bounded extendable functions.
منابع مشابه
O ct 1 99 4 Cardinal invariants concerning functions whose sum is almost continuous
Cardinal invariants concerning functions whose sum is almost continuous. Abstract Let A stand for the class of all almost continuous functions from R to R and let A(A) be the smallest cardinality of a family F ⊆ R R for which there is no g: R → R with the property that f + g ∈ A for all f ∈ F. We define cardinal number A(D) for the class D of all real functions with the Darboux property similar...
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