Cardinal invariants concerning bounded families of extendable and almost continuous functions
نویسندگان
چکیده
منابع مشابه
Cardinal Invariants concerning Bounded Families of Extendable and Almost Continuous Functions
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 f...
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The main purpose of this paper is to describe two examples. The first is that of an almost continuous, Baire class two, non-extendable function f : [0, 1] → [0, 1] with a Gδ graph. This answers a question of Gibson [15]. The second example is that of a connectivity function F : R → R with dense graph such that F−1(0) is contained in a countable union of straight lines. This easily implies the e...
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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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In this note we will construct, under the assumption that union of less than continuum many meager subsets of R is meager in R, an additive connectivity function f : R → R with Cantor intermediate value property which is not almost continuous. This gives a partial answer to a question of D. Banaszewski [2]. (See also [12, Question 5.5].) We will also show that every extendable function g : R → ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1998
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-98-04098-2