جستجوی مقالات مرتبط با کلیدواژه
تکرار جستجوی کلیدواژه integer-valued continuous functions on frames در نشریات گروه علوم پایه
integer-valued continuous functions on frames
در نشریات گروه ریاضی
تکرار جستجوی کلیدواژه integer-valued continuous functions on frames در مقالات مجلات علمی
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Categories and General Algebraic Structures with Applications, Volume:11 Issue: 1, Jul 2019, PP 19 -32This paper establishes two new connections between the familiar function ring functor ${mathfrak R}$ on the category ${bf CRFrm}$ of completely regular frames and the category {bf CR}${mathbf sigma}${bf Frm} of completely regular $sigma$-frames as well as their counterparts for the analogous functor ${mathfrak Z}$ on the category {bf ODFrm} of 0-dimensional frames, given by the integer-valued functions, and for the related functors ${mathfrak R}^*$ and ${mathfrak Z}^*$ corresponding to the bounded functions. Further it is shown that some familiar facts concerning these functors are simple consequences of the present results.Keywords: Completely regular frames, zero dimensional frames, completely regular σ-frames, zero dimensional σ-frames, real-valued continuous functions, integer-valued continuous functions on frames
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Categories and General Algebraic Structures with Applications, Volume:1 Issue: 1, Dec 2013, PP 1 -10For any archimedeanf-ring A with unit in whichbreakawedgeýý(1−a)leq0 for all ainAý, ýthe following are shown to beý ýequivalentý: ý ý1ý. ýA is isomorphic to the l-ring mathfrakZL of allý ýinteger-valued continuous functions on some frame Lý. 2ý. ýA is a homomorphic image of the l-ring CBbbZ(X)ý ýof all integer-valued continuous functionsý, ýin the usual senseý, ýon some topological space Xý. 3ý. ýFor any family (an)ninomega in A there exists aný ýl-ring homomorphism breakvarphiý:ýCBbbZ(BbbýýZomega)rightarrowA such that varphi(pn)=an for theý ýproduct projections breakpn:BbbZomegarightarrowBbbZ ý. ýThis provides an integer-valued counterpart to a familiar resultý ýconcerning real-valued continuous functionsýKeywords: Frames, 0-dimensional frames, integer-valued continuous functions on frames, archimedean mathbbZ -rings, countable mathbbZ-composition closedness
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