On sums of real-valued functions with extremely thick graphs
نویسندگان
چکیده
منابع مشابه
The ring of real-valued functions on a frame
In this paper, we define and study the notion of the real-valued functions on a frame $L$. We show that $F(L) $, consisting of all frame homomorphisms from the power set of $mathbb{R}$ to a frame $ L$, is an $f$-ring, as a generalization of all functions from a set $X$ into $mathbb R$. Also, we show that $F(L) $ is isomorphic to a sub-$f$-ring of $mathcal{R}(L)$, the ring of real-valued continu...
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Let $ { mathcal{R}} L$ be the ring of real-valued continuous functions on a frame $L$ as the pointfree version of $C(X)$, the ring of all real-valued continuous functions on a topological space $X$. Since $C_c(X)$ is the largest subring of $C(X)$ whose elements have countable image, this motivates us to present the pointfree version of $C_c(X).$The main aim of this paper is to present t...
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We develop the flow analog of the classical Yosida adjunction between spaces and archimedean lattice-ordered groups with strong unit. A product of this development is the flow counterpart of the classical compactification of a space. We characterize those flows which are compactifiable, i.e., dense subflows of a compact flow. Finally, we exhibit a duality between the compactifications of a give...
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A frame $L$ is called {it coz-dense} if $Sigma_{coz(alpha)}=emptyset$ implies $alpha=mathbf 0$. Let $mathcal RL$ be the ring of real-valued continuous functions on a coz-dense and completely regular frame $L$. We present a description of the socle of the ring $mathcal RL$ based on minimal ideals of $mathcal RL$ and zero sets in pointfree topology. We show that socle of $mathcal RL$ is an essent...
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ژورنال
عنوان ژورنال: Expositiones Mathematicae
سال: 2009
ISSN: 0723-0869
DOI: 10.1016/j.exmath.2008.10.003