On the locally fine construction in uniform spaces, locales and formal spaces
On the locally fine construction in uniform spaces, locales and formal spaces
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论统一空间、场所和形式空间中的局部精细构造
DOI：
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发表时间：
2005
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通讯作者：
Aarno Hohti
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作者：
Aarno Hohti
.我们研究了locale乘积的空间性与作者早期关于一致空间乘积的局部精细核映射的研究之间的联系。在给出一个历史性的介绍并指出空间性和局部精细结构之间的联系之后，我们指出早期的结果如何直接解决T.拜托最后，我们建立了拓扑（完全正则）空间的局部乘积的覆盖幺半群与（有限）一致空间的相应乘积的局部有限核映射之间的一般同构。此外，本文还通过展示覆盖关系的传递性如何对应于局部精细构造，来联系最近对形式拓扑和一致空间的研究。
. We investigate the connection between the spatiality of locale products and the earlier studies of the author on the locally fine coreflection of the products of uniform spaces. After giving a historical introduction and indicating the connection between spatiality and the locally fine construction, we indicate how the earlier results directly solve the first of the two open problems announced in the thesis of T. Plewe. Finally, we establish a general isomorphism between the covering monoids of the localic product of topological (completely regular) spaces and the locally fine coreflection of the corresponding product of (fine) uniform spaces. Additionally, paper relates the recent studies on formal topology and uniform spaces by showing how the transitivity of covering relations corresponds to the locally fine construction.