The function ring functors of pointfree topology revisited
This 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...
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| Format: | Article |
| Language: | English |
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Shahid Beheshti University
2019-07-01
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| Series: | Categories and General Algebraic Structures with Applications |
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| Online Access: | https://cgasa.sbu.ac.ir/article_87117_d2e1481a97bb9235d4ea8ec563e32744.pdf |
| Summary: | This 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. |
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| ISSN: | 2345-5853 2345-5861 |