L-偏序集映射空间连续性的刻画
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摘要
设L为完备剩余格,在L-偏序集中引入步函数的概念。基于一般的weight类,得到了L-偏序集映射空间连续性的一个刻画定理。基于以上结果,证明了两个完全代数的L-完备格之间的余连续映射之集是完全代数的。
Let Lbe a complete residuated lattice.By introducing the concept of step function in Lposets,a characterization theorem for the continuity of function spaces of L-posets with respect to a general choice of a class of weights is proved.Based on this,it is obtained that for two totally algebraic complete L-posets the set of all cocontinuous functions between them is totally algebraic.
Let Lbe a complete residuated lattice.By introducing the concept of step function in Lposets,a characterization theorem for the continuity of function spaces of L-posets with respect to a general choice of a class of weights is proved.Based on this,it is obtained that for two totally algebraic complete L-posets the set of all cocontinuous functions between them is totally algebraic.
引文
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[2]RUTTEN J M.Elements of generalized ultrametric domain theory[J].Theoretical Computer Science,1996,170(1/2):349-381.
[3]WAGNER K R.Solving recursive domain equations with enriched categories[D].Pittsburgh:School of Com-puter Science,Carnegie-Mellon University,1994.
[4]WAGNER K R.Liminf convergence inΩ-categories[J].Theoretical Computer Science,1997,184(1/2):61-104.
[5]FAN L.A new approach to quantitative domain theory[J].Electronic Notes in Theoretical Computer Science,2001,45:77-87.
[6]HOFMANN D,WASZKIEWICZ P L.Approximation in quantale-enriched categories[J].Topology and its Applications,2011,158(8):963-977.
[7]LAWVERE F W.Metric spaces,generalized logic,and closed categories[J].Rendiconti del Seminario Matematico e Fisico di Milano,1973,43:135-166.
[8]KELLY G M.Basic concepts of enriched category theory[M].Cambridge:Cambridge University Press,1982.
[9]STUBBE I.Categorical structures enriched in a quantaloid:categories,distributors and functors[J].Theory and Applications of Categories,2005,14:1-45.
[10]STUBBE I.Categorical structures enriched in a quantaloid:tensored and cotensored categories[J].Theory and Applications of Categories,2006,16:283-306.
[11]STUBBE I.Towardsdynamic domains":totally continuous cocomplete Q-categories[J].Theoretical Computer Science,2007,373:142-160.
[12]LAI H L,ZHANG D X.Complete and directed completeΩ-categories[J].Theoretical Computer Science,2007,388(1/2/3):1-25.
[13]LAI H L,ZHANG D X.Many-valued complete distributivity[EB/OL].[2017-03-01].https:∥arxiv.org/pdf/math/0603590.
[14]赖洪亮.Ω-范畴序结构性质的研究[D].成都:四川大学数学学院,2007.
[15]ZHANG D X.An enriched category approach to many valued topology[J].Fuzzy Sets and Systems,2007,158:349-366.
[16]ROSENTHAL K I.Quantales and their applications[M].New York:Longman Scientific&Technical,1990.
[17]ZHANG Q Y,FAN L.Continuity in quantitative domains[J].Fuzzy Sets and Systems,2005,154(1):118-131.
[18]YAO W.Quantitative domains via fuzzy sets:Part I:continuity of fuzzy directed-complete poset[J].Fuzzy Sets and Systems,2010,161(7):973-987.
[19]GUO L K,ZHANG G Q,LI Q G.Fuzzy closure systems on L-ordered sets[J].Mathematical Logic Quarterly,2011,57(3):281-291.
[20]RAO S P,LI Q G.Fuzzy Z-continuous posets[J].Abstract and Applied Analysis,2013(3):41-62.
[21]BELOHLAVEK R.Fuzzy relational systems:foundations and principles[M].New York:Kluwer Academic Publishers,Plenum Publishers,2002.