| 孟华,寇辉.关于交半格同态构成的函数空间与FS-交连续Domain[J].数学年刊A辑,2011,32(1):107~114 |
| 关于交半格同态构成的函数空间与FS-交连续Domain |
| On the Function Spaces of Semilattice Homomorphisms and FS^-Domains |
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| DOI： |
| 中文关键词: FS-交连续domain 有界完备domain 函数空间 幂domain |
| 英文关键词: |
| 基金项目:国家自然科学基金(No.10871137); 教育部新世纪优秀人才支持计划(No.070576)资助的项目 |
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| 中文摘要: |
| 定义了一类序结构\!---$FS$-交连续domain, 讨论其相关性质并证明:\!(1) $FS$-交连续domain关于由Scott连续且保持非空有限交运算的函数构成的函数空间封闭,
以(代数) $FS$-交连续domain为对象、以Scott连续函数为态射的范畴是Cartesian闭范畴;\!(2)任意分配可乘的有界完备domain是$FS$-交连续domain,
从而紧连续dcpo的Smyth幂domain是$FS$-交连续domain. 这些结果表明, $FS$-交连续domain是关于保非空有限交的连续映射构成的函数空间封闭的最恰当序结构. |
| 英文摘要: |
| The authors define an order structure named as $FS_{\wedge}$-domain and investigate its (category) properties.
It is shown that (1) $FS_{\wedge}$-domains are closed under the function spaces consisting of semilattice homomorphisms, i.e.,
Scott continuous functions preserving meets; (2) Every distributive bounded complete domain which is multiplicative
(about $\ll$) is an $FS_{\wedge}$-domain. Particularly, the Smyth powerdomain of a Lawson-compact continuous
domain is an $FS_{\wedge}$-domain. These results show that the $FS_{\wedge}$-domain is the most suitable
continuous semilattice closed under the function spaces of semilattice homomorphisms. |
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