نتایج جستجو برای: ring of real valued continuous functions on a frame
تعداد نتایج: 23904219 فیلتر نتایج به سال:
in this paper a particular case of z-ideals, called strongly z-ideal, is defined by introducing zero sets in pointfree topology. we study strongly z-ideals, their relation with z-ideals and the role of spatiality in this relation. for strongly z-ideals, we analyze prime ideals using the concept of zero sets. moreover, it is proven that the intersection of all zero sets of a prime ideal of c(l),...
let $l$ be a completely regular frame and $mathcal{r}l$ be the ring of continuous real-valued functions on $l$. we show that the lattice $zid(mathcal{r}l)$ of $z$-ideals of $mathcal{r}l$ is a normal coherent yosida frame, which extends the corresponding $c(x)$ result of mart'{i}nez and zenk. this we do by exhibiting $zid(mathcal{r}l)$ as a quotient of $rad(mathcal{r}l)$, the ...
section{introduction} the concept of {sl cartan geometry} appeared at the beginning of the twentieth century, when {e}lie cartan was working on the so-called {sl equivalence problem}, the aim of which is to determine whether two given geometric structures can be mapped bijectively onto each other by some diffeomorphism. this problem can be considered in many different contexts, such as ...
In this paper a particular case of z-ideals, called strongly z-ideal, is defined by introducing zero sets in pointfree topology. We study strongly z-ideals, their relation with z-ideals and the role of spatiality in this relation. For strongly z-ideals, we analyze prime ideals using the concept of zero sets. Moreover, it is proven that the intersection of all zero sets of a prime ideal of C(L),...
Let $L$ be a completely regular frame and $mathcal{R}L$ be the ring of continuous real-valued functions on $L$. We show that the lattice $Zid(mathcal{R}L)$ of $z$-ideals of $mathcal{R}L$ is a normal coherent Yosida frame, which extends the corresponding $C(X)$ result of Mart'{i}nez and Zenk. This we do by exhibiting $Zid(mathcal{R}L)$ as a quotient of $Rad(mathcal{R}L)$, the ...
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 ...
In pointfree topology, a continuous real function on a frame L is a map L(R) → L from the frame of reals into L. The discussion of continuous real functions with possibly infinite values can be easily brought to pointfree topology by replacing the frame L(R) with the frame of extended reals L ( R ) (i.e. the pointfree counterpart of the extended real line R = R ∪ {±∞}). One can even deal with a...
In this paper, we define and study the notion of zero elements in topoframes; a topoframe is a pair $(L, tau)$, abbreviated $L_{ tau}$, consisting of a frame $L$ and a subframe $ tau $ all of whose elements are complemented elements in $L$. We show that the $f$-ring $ mathcal{R}(L_tau)$, the set of $tau$-real continuous functions on $L$, is uniformly complete. Also, t...
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