countable composition closedness and integer-valued continuous functions in pointfree topology
نویسندگان
چکیده
for any archimedean$f$-ring $a$ with unit in whichbreak$awedge(1-a)leq 0$ for all $ain a$, the following are shown to beequivalent:1. $a$ is isomorphic to the $l$-ring ${mathfrak z}l$ of allinteger-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$varphi :c_{bbb z}(bbbz^omega)rightarrow a$ such that $varphi(p_n)=a_n$ for theproduct projections break$p_n:{bbb z^omega}rightarrow bbb z$.this provides an integer-valued counterpart to a familiar resultconcerning real-valued continuous functions.
منابع مشابه
Countable composition closedness and integer-valued continuous functions in pointfree topology
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 se...
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عنوان ژورنال:
categories and general algebraic structures with applicationsناشر: shahid beheshti university
ISSN 2345-5853
دوره 1
شماره 1 2013
کلمات کلیدی
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