Decomposing symmetrically continuous and Sierpinski-Zygmund functions into continuous functions
نویسندگان
چکیده
منابع مشابه
Decomposing Symmetrically Continuous and Sierpiński-zygmund Functions into Continuous Functions
In this paper we will investigate the smallest cardinal number κ such that for any symmetrically continuous function f : R → R there is a partition {Xξ : ξ < κ} of R such that every restriction f Xξ : Xξ → R is continuous. The similar numbers for the classes of Sierpiński-Zygmund functions and all functions from R to R are also investigated and it is proved that all these numbers are equal. We ...
متن کاملSierpinski-Zygmund functions that are Darboux, almost continuous, or have a perfect road
In this paper we show that if the real line R is not a union of less than continuum many of its meager subsets then there exists an almost continuous Sierpiński–Zygmund function having a perfect road at each point. We also prove that it is consistent with ZFC that every Darboux function f :R→ R is continuous on some set of cardinality continuum. In particular, both these results imply that the ...
متن کاملContra $beta^{*}$-continuous and almost contra $beta^{*}$-continuous functions
The notion of contra continuous functions was introduced and investigated by Dontchev. In this paper, we apply the notion of $beta^{*}$-closed sets in topological space to present and study a new class of functions called contra $beta^{*}$-continuous and almost contra $beta^{*}$-continuous functions as a new generalization of contra continuity.
متن کاملGeneralized Rings of Measurable and Continuous Functions
This paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.
متن کاملContinuity of super- and sub-additive transformations of continuous functions
We prove a continuity inheritance property for super- and sub-additive transformations of non-negative continuous multivariate functions defined on the domain of all non-negative points and vanishing at the origin. As a corollary of this result we obtain that super- and sub-additive transformations of continuous aggregation functions are again continuous aggregation functions.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1999
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-99-04955-2