التفاصيل البيبلوغرافية
| العنوان: |
Examples of Sierpiński–Zygmund maps in the class of Darboux-like functions. |
| المؤلفون: |
Ciesielski, Krzysztof Chris1,2 (AUTHOR) KCies@math.wvu.edu, Pan, Cheng-Han1 (AUTHOR) |
| المصدر: |
Banach Journal of Mathematical Analysis. Apr2020, Vol. 14 Issue 2, p433-449. 17p. |
| مصطلحات موضوعية: |
SET theory, ALGEBRA, ATOMS, CONTINUOUS functions, INTERSECTION theory |
| مستخلص: |
The Darboux-like functions represent a group of maps that are continuous in a generalized sense. The algebra of subsets of R R (i.e., maps from R to R ) generated by these classes has nine atoms, that is, the smallest non-empty elements of the algebra. The subject of this work is to study the intersections of these atoms with the class SZ of Sierpiński–Zygmund functions—the maps that have as little of the standard continuity as possible. Specifically, we will show that it is independent of the standard axioms of set theory that each of these atoms has a non-empty intersection with SZ . For seven of the nine atoms this has been unknown, and the constructions of the examples provide answers to the problems stated in a recent survey A century of Sierpiński–Zygmund functions of K. C. Ciesielski and J. Seoane-Sepúlveda. Notice that lineability of the main classes of Darboux-like functions, as well as of Sierpiński–Zygmund functions, has been intensively studied. The presented work opens a possibility to study also the lineability of the nine smaller classes we discuss here. [ABSTRACT FROM AUTHOR] |
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| قاعدة البيانات: |
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