@article {
author = {Banaschewski, Bernhard},
title = {Countable composition closedness and integer-valued continuous functions in pointfree topology},
journal = {Categories and General Algebraic Structures with Applications},
volume = {1},
number = {1},
pages = {1-10},
year = {2013},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {},
abstract = {For any archimedean$f$-ring $A$ with unit in whichbreak$awedge (1-a)leq 0$ for all $ain A$, the following are shown to be equivalent: 1. $A$ is isomorphic to the $l$-ring ${mathfrak Z}L$ of all integer-valued continuous functions on some frame $L$. 2. $A$ is a homomorphic image of the $l$-ring $C_{Bbb Z}(X)$ of all integer-valued continuous functions, in the usual sense, on some topological space $X$. 3. For any family $(a_n)_{nin omega}$ in $A$ there exists an $l$-ring homomorphism break$varphi :C_{Bbb Z}(Bbb Z^omega)rightarrow A$ such that $varphi(p_n)=a_n$ for the product projections break$p_n:{Bbb Z^omega}rightarrow Bbb Z$. This provides an integer-valued counterpart to a familiar result concerning real-valued continuous functions.},
keywords = {Frames,0-dimensional frames,integer-valued continuous
functions on frames,archimedean ${mathbb Z}$-rings,countable
$mathbb {Z}$-composition closedness},
url = {https://cgasa.sbu.ac.ir/article_4262.html},
eprint = {https://cgasa.sbu.ac.ir/article_4262_73b32f9f16cd67536694bb804916b55f.pdf}
}