View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by The Research Repository @ WVU (West Virginia University) Faculty Scholarship 1995 Cardinal Invariants Concerning Functions Whose Sum Is Almost Continuous Krzysztof Ciesielski West Virginia University,
[email protected] Follow this and additional works at: https://researchrepository.wvu.edu/faculty_publications Part of the Mathematics Commons Digital Commons Citation Ciesielski, Krzysztof, "Cardinal Invariants Concerning Functions Whose Sum Is Almost Continuous" (1995). Faculty Scholarship. 822. https://researchrepository.wvu.edu/faculty_publications/822 This Article is brought to you for free and open access by The Research Repository @ WVU. It has been accepted for inclusion in Faculty Scholarship by an authorized administrator of The Research Repository @ WVU. For more information, please contact
[email protected]. Cardinal invariants concerning functions whose sum is almost continuous. Krzysztof Ciesielski1, Department of Mathematics, West Virginia University, Mor- gantown, WV 26506-6310 (
[email protected]) Arnold W. Miller1, York University, Department of Mathematics, North York, Ontario M3J 1P3, Canada, Permanent address: University of Wisconsin-Madison, Department of Mathematics, Van Vleck Hall, 480 Lincoln Drive, Madison, Wis- consin 53706-1388, USA (
[email protected]) 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 ⊆ RR 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 similarly.