Algebraic operations on the space of Hausdorff continuous interval functions
نویسنده
چکیده
We show that the operations addition and multiplication on the set C(Ω) of all real continuous functions on Ω ⊆ Rn can be extended to the set H(Ω) of all Hausdorff continuous interval functions on Ω in such a way that the algebraic structure of C(Ω) is preserved, namely, H(Ω) is a commutative ring with identity. The operations on H(Ω) are defined in three different but equivalent ways. This allow us to look at these operations from different points of view as well as to show that they are naturally associated with the Hausdorff continuous functions.
منابع مشابه
Algebraic Computations with Hausdorff Continuous Functions
The set of Hausdorff continuous functions is the largest set of interval valued functions to which the ring structure of the set of continuous real functions can be extended. The paper deals with the automation of the algebraic operations for Hausdorff continuous functions using an ultraarithmetical approach.
متن کاملNumerical Computations with Hausdorff Continuous Functions
Hausdorff continuous (H-continuous) functions appear naturally in many areas of mathematics like Approximation Theory [11], Real Analysis [1], [8], Interval Analysis, [2], etc. From numerical point of view it is significant that the solutions of large classes of nonlinear partial differential equations can be assimilated through H-continuous functions [7]. As a particular case the discontinuous...
متن کاملThe ring of real-continuous functions on a topoframe
A topoframe, denoted by $L_{ tau}$, is a pair $(L, tau)$ consisting of a frame $L$ and a subframe $ tau $ all of whose elements are complementary elements in $L$. In this paper, we define and study the notions of a $tau $-real-continuous function on a frame $L$ and the set of real continuous functions $mathcal{R}L_tau $ as an $f$-ring. We show that $mathcal{R}L_{ tau}$ is actually a generali...
متن کاملHausdorff Continuous Interval Functions and Approximations
The set of interval Hausdorff continuous functions constitutes the largest space preserving basic algebraic and topological structural properties of continuous functions, such as linearity, ring structure, Dedekind order completeness, etc. Spaces of interval functions have important applications not only in the construction of numerical methods and algorithms, but to problems in abstract areas ...
متن کامل$z^circ$-filters and related ideals in $C(X)$
In this article we introduce the concept of $z^circ$-filter on a topological space $X$. We study and investigate the behavior of $z^circ$-filters and compare them with corresponding ideals, namely, $z^circ$-ideals of $C(X)$, the ring of real-valued continuous functions on a completely regular Hausdorff space $X$. It is observed that $X$ is a compact space if and only if every $z^circ$-filter ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005